SUPPLEMENTARY FILE COUNTRY N LOCATIONS PERIOD MORTALITY DATA TEMPERATURE DATA. Non-external. Statistics) Non-external

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1 SUPPLEMENTARY FILE Table S1. Description of the data COUNTRY N LOCATIONS PERIOD MORTALITY DATA TEMPERATURE DATA Non-external Data from meteorological Australia 3 cities causes only stations located within 30 (Australian Bureau of km of each city s (Australian Statistics) Bureau of Meteorology) Brazil 18 cities Canada Island of Ireland 24 census metropolitan areas (CMA) and 1 city (Hamilton) 6 regions covering all Island population (ROI) and two in the Northern Ireland (NI)) Japan 47 prefectures South Korea 7 cities Spain 50 capital cities Switzerland UK 7 cities and 1 metropolitan area (Lugano) 9 regions in England and Wales USA 135 cities Non-external causes only (Ministry of Health) All causes (Canadian Mortality Database) Non-external causes only (Irish Central Statistics Office Northern and Ireland Social Research Agency for ROI and NI) All causes (Ministry of Health, Labour and Welfare) All causes (Korea Bureau of Statistics) All causes (Spain National Institute of Statistics) All causes (Federal Office of Statistics) All causes (Office of National Statistics) Non-external causes (National Center for Health Statistics) Weather station located within the urban area (National Institute of Meteorology of Brazil) Monitoring station located closest to the CMA centre (Environment Canada) Two weather stations for each of the four ROI regions and two weather stations for the two NI regions (Met Eireann, and the United Kingdom Meteorological Office for ROI and NI) Weather station located within the urban area of the capital city (Japan Meteorology Agency) Weather station located within the urban area (Korea Meteorological Administration) Weather station located within the urban area or at the near airport (Spain National Meteorology Agency) Weather station located within or near the urban area (Federal Office of Meteorology and Climatology) An average of 29 stations contributed data to each regional series (British Atmospheric Data Centre) Weather station closest to the city centre (National Climatic Data Center)

2 Table S2. List of the 305 locations in 10 countries with study periods, total number of deaths and mean daily temperature (mean and range). LOCATION COUNTRY PERIOD TOTAL DEATHS TMEAN (MEAN[RANGE]) Brisbane Australia [7.4 ; 31.4] Melbourne Australia [5.6 ; 35] Sydney Australia [7.8 ; 31.8] Belem Brazil [23.4 ; 29.4] Belo Horizonte Brazil [11.9 ; 29.5] Brasilia Brazil [14.1 ; 29.1] Cuiaba Brazil [11.4 ; 33.4] Curitiba Brazil [3.6 ; 27.4] Fortaleza Brazil [23.2 ; 29.7] Goiania Brazil [15.1 ; 32] Joao Pessoa Brazil [22.2 ; 30.3] Maceio Brazil [20.8 ; 29.1] Manaus Brazil [21.3 ; 32.8] Natal Brazil [21.8 ; 29.8] Porto Alegre Brazil [5.2 ; 33.5] Recife Brazil [21.8 ; 29.4] Salvador Brazil [20.3 ; 29.2] Sao Luis Brazil [23 ; 29.9] Sao Paulo Brazil [7.8 ; 28.6] Teresina Brazil [22.4 ; 32.5] Vitoria Brazil [16.2 ; 31.4] Abbotsford Canada [-12.9 ; 29] Calgary Canada [-33.9 ; 24.3] Edmonton Canada [-39.7 ; 29.4] Halifax Canada [-23.5 ; 26.6] Hamilton Canada [-24.1 ; 29.6] Kingston Canada [-26 ; 29.5] Kitchener-Waterloo Canada [-25.2 ; 29.8] London Ontario Canada [-24.7 ; 30.7] Niagara Canada [-21 ; 30.5] Oakville Canada [-21.9 ; 31.1] Oshawa Canada [-26.1 ; 30.2] Ottawa Canada [-28.4 ; 29.7] Regina Canada [-36.5 ; 31.4] Sarnia Canada [-24.9 ; 30.7] Sudbury Canada [-33.8 ; 28.8] Saint John NB Canada [-25 ; 25.7] St. John's NFL Canada [-21.3 ; 24.3] Sault Ste. Marie Canada [-29.6 ; 27.7] Saskatoon Canada [-38.9 ; 32.1]

3 Thunder Bay Canada [-33.6 ; 27.3] Toronto Canada [-24.7 ; 31.5] Victoria Canada [-10.4 ; 26.7] Vancouver Canada [-10.7 ; 28.4] Windsor Canada [-25 ; 31.5] Winnipeg Canada [-38.6 ; 30.9] West of Northern Ireland Ireland [-6.2 ; 22.1] Ballywatticock and Banagher Ireland [-3.7 ; 21.4] Birr and Kilkenny Ireland [-5.4 ; 22.9] Dublin and Casement Ireland [-4.5 ; 21.6] Malin and Clones Ireland [-5.4 ; 21.2] Roslare, Cork, Valentia and Shannon Ireland [-4.1 ; 21.8] Aichi Japan [-2 ; 32.7] Akita Japan [-6.1 ; 31.6] Aomori Japan [-8.2 ; 30.1] Chiba Japan [0.3 ; 32.2] Ehime Japan [-0.7 ; 31.9] Fukushima Japan [-4.7 ; 31.4] Fukuoka Japan [-0.8 ; 32.4] Fukui Japan [-2.7 ; 32.1] Gifu Japan [-2.1 ; 32.9] Gunma Japan [-2.1 ; 32.6] Hokkaido Japan [-12 ; 30.1] Hiroshima Japan [-2.1 ; 32.7] Hyogo Japan [-1.5 ; 32] Ibaraki Japan [-3.8 ; 31.3] Ishikawa Japan [-2.6 ; 32.3] Iwate Japan [-8.9 ; 29.3] Kagawa Japan [-0.7 ; 32.3] Kagoshima Japan [0.1 ; 31.1] Kumamoto Japan [-1.8 ; 31.5] Kanagawa Japan [0.5 ; 30.9] Kochi Japan [-0.7 ; 32.1] Kyoto Japan [-1.2 ; 32.8] Mie Japan [-0.8 ; 33.5] Miyagi Japan [-4.8 ; 31.2] Miyazaki Japan [0.8 ; 32] Nagano Japan [-6.8 ; 30.7] Nara Japan [-1.7 ; 31.7] Nagasaki Japan [-0.8 ; 32.2] Niigata Japan [-3.7 ; 32.6] Oita Japan [-0.6 ; 31.6] Okinawa Japan [10 ; 31.1] Okayama Japan [-2.2 ; 32.3]

4 Osaka Japan [-0.1 ; 32.9] Saga Japan [-2.5 ; 32.2] Saitama Japan [-2.4 ; 33.7] Shiga Japan [-2.1 ; 31.4] Shimane Japan [-3.3 ; 32.2] Shizuoka Japan [0.8 ; 31.9] Tochigi Japan [-2.9 ; 31.4] Tokushima Japan [-1.3 ; 32.3] Tokyo Japan [0.5 ; 33.1] Toyama Japan [-3.7 ; 33.8] Tottori Japan [-3.1 ; 32.3] Wakayama Japan [-0.1 ; 31.9] Yamaguchi Japan [-4.5 ; 31.2] Yamagata Japan [-6.8 ; 31.1] Yamanashi Japan [-4.4 ; 31.8] Busan South Korea [-7.1 ; 30.2] Daegu South Korea [-8.5 ; 32.9] Daejeon South Korea [-12.6 ; 31.8] Gwangju South Korea [-9 ; 31.3] Incheon South Korea [-14.7 ; 31.4] Seoul South Korea [-15.7 ; 33] Ulsan South Korea [-7.4 ; 30.8] A Coruna Spain [2.4 ; 29] Albacete Spain [-10.7 ; 31.6] Alicante Spain [4 ; 32.2] Almeria Spain [5.4 ; 36.2] Avila Spain [-6.3 ; 28.6] Badajoz Spain [1.6 ; 33.9] Bilbao Spain [-0.4 ; 32.2] Barcelona Spain [1.4 ; 30.9] Burgos Spain [-9.8 ; 29.8] Cadiz Spain [3.9 ; 32.9] Caceres Spain [0.1 ; 34.1] Ciudad Real Spain [-3.2 ; 33.7] Cordoba Spain [1 ; 36.3] Castellon Spain [3.4 ; 32] Cuenca Spain [-4.4 ; 29.8] Guadalajara Spain [-3.8 ; 29] Girona Spain [-2.3 ; 30.4] Granada Spain [-3.1 ; 32.7] Huelva Spain [3.8 ; 36.2] Huesca Spain [-5.5 ; 32] Jaen Spain [-3.1 ; 35.3] Leon Spain [-8.5 ; 27.9] Logrono Spain [-4.9 ; 31.5]

5 Lleida Spain [-7.6 ; 30.6] Lugo Spain [-4.1 ; 29.1] Malaga Spain [4.4 ; 34.2] Madrid Spain [-1.8 ; 32.4] Melilla Spain [3.8 ; 36.1] Murcia Spain [3.8 ; 36.1] Ourense Spain [-1.3 ; 31.5] Oviedo Spain [-1.6 ; 28.4] Palmas G. Canaria Spain [13.7 ; 33.4] Palma Mallorca Spain [1.8 ; 32.1] Pamplona Spain [-5.2 ; 31.6] Pontevedra Spain [2.4 ; 30.4] Segovia Spain [-6.3 ; 31.4] Salamanca Spain [-5.1 ; 29.1] San Sebastian Spain [-1.7 ; 30.3] Santander Spain [1.1 ; 27.8] Soria Spain [-7.2 ; 28.1] Sevilla Spain [2.7 ; 36.8] Teruel Spain [-10.9 ; 27.8] Tenerife Spain [13.4 ; 34.3] Toledo Spain [-2 ; 34] Tarragona Spain [-0.1 ; 32.4] Vitoria Spain [-6.4 ; 30.6] Valladolid Spain [-4.8 ; 30.9] Valencia Spain [3.4 ; 33.8] Zamora Spain [-4.3 ; 30.8] Zaragoza Spain [-4.8 ; 32.9] Basel Switzerland [-12.4 ; 29] Bern Switzerland [-14.2 ; 25.9] Geneva Switzerland [-9.2 ; 28.8] Lausanne Switzerland [-10.3 ; 28.9] Lugano Switzerland [-5.3 ; 28.2] Luzern Switzerland [-11.6 ; 26.6] St. Gallen Switzerland [-14.9 ; 27.0] Zurich Switzerland [-13.5 ; 27.7] East UK [-6 ; 25.2] East Midlands UK [-6.4 ; 25.3] London UK [-5.5 ; 29.1] North East UK [-5.2 ; 25] North West UK [-5.7 ; 23.7] South East UK [-6.3 ; 25.3] South West UK [-5.8 ; 24.8] Wales UK [-4.7 ; 24] West Midlands UK [-7.4 ; 25] Yorkshire & Humber UK [-6.2 ; 26.1]

6 Akron, OH USA [-26.7 ; 30.8] Albuquerque, NM USA [-14.7 ; 32.2] Allentown-Bethlehem, PA USA [-20.6 ; 31.4] Austin, TX USA [-8.6 ; 35] Atlantic City, NJ USA [-18.1 ; 32.2] Atlanta, GA USA [-15 ; 32.5] Buffalo, NY USA [-21.1 ; 30.3] Bakersfield, CA USA [-1.9 ; 36.7] Baltimore, MD USA [-17.8 ; 32.5] Bergen-Passaic, NJ USA [-18.6 ; 34.7] Birmingham, AL USA [-13.3 ; 32.2] Barnstable-Yarmouth, MA USA [-17.2 ; 30.6] Baton Rouge, LA USA [-8.6 ; 32.8] Brownsville, TX USA [-3.9 ; 33.1] Boston, MA USA [-16.9 ; 32.2] Chicago, IL USA [-26.7 ; 33.6] Charleston, WV USA [-20.6 ; 31.7] Charlotte, NC USA [-12.5 ; 32.5] Chattanooga, TN USA [-15.8 ; 32.8] Columbus, OH USA [-24.4 ; 31.7] Cleveland, OH USA [-24.4 ; 30.8] Cincinnati, OH USA [-23.6 ; 33.1] Canton-Massillon, OH USA [-26.7 ; 30.8] Columbia, SC USA [-11.1 ; 32.8] Des Moines, IA USA [-27.5 ; 32.8] Dallas, TX USA [-13.1 ; 35.8] Denver, CO USA [-25.6 ; 30.3] Dutchess County, NY USA [-20.3 ; 31.7] Detroit, MI USA [-24.4 ; 31.4] Daytona Beach, FL USA [-3.3 ; 31.7] Dayton, OH USA [-27.5 ; 32.2] El Paso, TX USA [-8.6 ; 36.7] Erie, PA USA [-23.9 ; 30] Flint, MI USA [-24.4 ; 30.8] Fresno, CA USA [-2.8 ; 38.6] Ft. Lauderdale, FL USA [0 ; 30.8] Fort Myers-Cape Coral, FL USA [1.9 ; 31.4] Fort Pierce-Port St. Lucie, FL USA [-1.4 ; 30.8] Gary, IN USA [-27.8 ; 31.7] Greensboro, NC USA [-14.2 ; 30.6] Greenville, SC USA [-11.7 ; 32.8] Grand Rapids, MI USA [-24.4 ; 31.7] Hamilton, OH USA [-23.6 ; 33.1] Hartford, CT USA [-18.3 ; 31.1] Houston, TX USA [-8.1 ; 33.3]

7 Indianapolis, IN USA [-26.9 ; 32.2] Jacksonville, FL USA [-7.5 ; 32.5] Jersey City, NJ USA [-18.6 ; 34.7] Kansas City, MO-KS USA [-26.7 ; 33.9] Knoxville, TN USA [-21.1 ; 30.3] Lubbock, TX USA [-14.4 ; 35.6] Lakeland-Winter Haven, FL USA [-0.8 ; 32.2] Lancaster, PA USA [-19.7 ; 31.1] Lansing, MI USA [-23.3 ; 30.8] Louisville, KY USA [-22.8 ; 34.2] Little Rock, AR USA [-14.2 ; 35.3] Los Angeles, CA USA [6.1 ; 31.1] Las Vegas, NV-AZ USA [-5.6 ; 41.1] McAllen-Edinburg-Mission, TX USA [-3.6 ; 36.7] Middlesex, NJ USA [-17.5 ; 32.5] Madison, WI USA [-28.9 ; 32.8] Miami, FL USA [3.3 ; 31.4] Melbourne-Titusville-Palm Bay, FL USA [-0.3 ; 31.9] Milwaukee, WI USA [-27.2 ; 33.9] Memphis, TN USA [-16.7 ; 33.9] Monmouth-Ocean, NJ USA [-17.2 ; 31.9] Minneapolis-St. Paul, MN USA [-31.4 ; 32.5] Mobile, AL USA [-9.4 ; 32.8] Myrtle Beach, SC USA [-8.3 ; 33.3] Nashua, NH USA [-20.3 ; 30] Nassau-Suffolk, NY USA [-16.4 ; 32.2] Naples, FL USA [3.6 ; 30.8] Nashville, TN USA [-20.3 ; 32.5] Newburgh, NY USA [-19.7 ; 30.8] New Haven-Meriden, CT USA [-18.3 ; 31.1] New London, CT USA [-16.9 ; 31.1] Newark, NJ USA [-18.6 ; 34.7] New York, NY USA [-16.4 ; 34.4] Ocala, FL USA [-3.6 ; 32.2] Oklahoma City, OK USA [-17.8 ; 34.7] Oakland, CA USA [0.6 ; 27.8] Omaha, NE USA [-26.7 ; 33.3] Orlando, FL USA [-2.5 ; 32.2] Orange County, CA USA [5.3 ; 32.8] Philadelphia, PA-NJ USA [-17.5 ; 33.3] Phoenix, AZ USA [2.5 ; 41.4] Pensacola, FL USA [-9.2 ; 34.2] Punta Gorda, FL USA [3.6 ; 32.2] Portland, ME USA [-20.3 ; 29.7]

8 Portland, OR USA [-11.1 ; 29.7] Providence-Fall River, RI-MA USA [-16.7 ; 31.4] Pittsburgh, PA USA [-25 ; 30.3] Rochester, NY USA [-21.1 ; 30.3] Rockford, IL USA [-28.3 ; 31.7] Reading, PA USA [-15.6 ; 32.2] Raleigh, NC USA [-15.6 ; 32.2] Riverside-San Bernardino, CA USA [3.6 ; 36.7] Sacramento, CA USA [-2.5 ; 34.7] Scranton--Wilkes-Barre-- Hazleton, PA USA [-22.2 ; 31.9] San Diego, CA USA [6.4 ; 30.8] San Francisco, CA USA [0.3 ; 30] Saginaw, MI USA [-23.9 ; 31.1] Shreveport, LA USA [-10 ; 34.2] San Jose, CA USA [-1.9 ; 32.2] Salinas, CA USA [0.6 ; 27.8] Salt Lake City, UT USA [-20 ; 32.8] San Antonio, TX USA [-7.8 ; 34.2] Spokane, WA USA [-23.6 ; 30.6] Springfield, MA USA [-18.3 ; 31.1] Sarasota-Bradenton, FL USA [0.8 ; 32.8] Stockton-Lodi, CA USA [-3.3 ; 36.9] St. Louis, MO-IL USA [-22.8 ; 33.6] Stamford-Norwalk, CT USA [-16.1 ; 30.8] Seattle, WA USA [-9.7 ; 28.1] Syracuse, NY USA [-23.6 ; 30.3] Tacoma, WA USA [-9.4 ; 26.7] Tampa-St. Petersburg- Clearwater, FL USA [-1.1 ; 31.7] Tucson, AZ USA [-1.4 ; 37.2] Toledo, OH USA [-25 ; 31.7] Trenton, NJ USA [-16.4 ; 31.7] Tulsa, OK USA [-17.5 ; 35.3] Utica-Rome, NY USA [-25.8 ; 28.9] Ventura County, CA USA [3.6 ; 29.2] Virginia Beach, VA USA [-15 ; 33.1] Wichita, KS USA [-22.2 ; 33.9] Wilmington, DE USA [-18.9 ; 31.9] West Palm Beach-Boca Raton, FL USA [1.7 ; 31.1] Worcester, MA USA [-21.1 ; 28.9] Washington, DC-MD-VA USA [-16.7 ; 33.9] Youngstown-Warren, OH USA [-25.6 ; 30.6] York, PA USA [-22.2 ; 31.1]

9 Table S3. Results obtained from the sensitivity analysis using three different combinations of specifications defining the cross-basis of daily mean temperature. Temporal changes in cold- and heat-mortality associations: relative risk (RR) and 95% confidence interval (CI) for cold and heat, temperature of minimum mortality (MMT) and minimum mortality percentile (MMP) for the first and last year of each country-specific series. Sensitivity 1 Sensitivity 2 Sensitivity 3 Country Year MMT[MMP] RR Cold RR Heat MMT[MMP] RR Cold RR Heat MMT[MMP] RR Cold RR Heat Australia first 27.4 [99] [1.530;2.204] last 17.6 [50] [0.931;1.181] Brazil first 25.4 [67] [1.198;1.347] last 24.9 [57] [1.151;1.294] Canada first 18.9 [90] [1.060;1.249] last 20.1 [91] [1.042;1.203] Ireland first 15.3 [94] [1.563;1.943] last 17.1 [99] [1.152;1.472] Japan first 27 [90] [1.279;1.398] last 28.1 [92] [1.327;1.417] South Korea first 25.6 [92] [0.832;1.102] last 26.9 [91] [1.218;1.577] Spain first 20 [70] [1.325;1.461] last 24.9 [91] [1.059;1.194] Switzerland first 10.7 [50] [1.168;1.539] last 20.7 [92] [0.994;1.516] UK first 18.2 [93] [1.296;1.428] [1.000;1.000] [1.105;1.374] [1.029;1.146] [1.020;1.125] [1.087;1.223] [0.996;1.089] [0.937;1.126] [1.000;1.000] [1.147;1.221] [0.993;1.025] [0.998;1.151] [1.005;1.177] [1.233;1.380] [1.128;1.225] [1.056;1.567] [0.948;1.379] [1.033;1.108] 24.1 [92] [1.558;2.066] 19.2 [61] [0.930;1.190] 25.6 [70] [1.197;1.343] 24.8 [55] [1.153;1.290] 16 [78] [1.076;1.256] 18.3 [83] [1.057;1.210] 17.3 [99] [1.438;1.882] 17.1 [99] [1.145;1.443] 22.8 [78] [1.332;1.451] 27 [88] [1.338;1.432] 22.9 [82] [0.817;1.072] 24.3 [80] [1.252;1.608] 21.4 [76] [1.339;1.487] 21.2 [76] [1.050;1.170] 10.9 [51] [1.171;1.545] 17.7 [78] [0.981;1.402] 15.1 [82] [1.247;1.370] [0.902;1.121] [1.106;1.363] [1.036;1.148] [1.011;1.105] [1.088;1.233] [1.002;1.106] [1.000;1.000] [1.000;1.000] [1.139;1.209] [0.985;1.014] [1.024;1.206] [0.949;1.107] [1.277;1.420] [1.116;1.221] [1.084;1.524] [0.931;1.249] [1.033;1.110] 27.4 [99] [1.511;2.145] 17.6 [50] [0.937;1.186] 25.3 [66] [1.199;1.346] 24.9 [56] [1.150;1.291] 16.5 [80] [1.046;1.219] 21.3 [95] [1.033;1.203] 15.8 [96] [1.587;2.002] 17.1 [99] [1.141;1.463] 28.1 [95] [1.253;1.376] 28.9 [96] [1.329;1.422] 26.8 [96] [0.835;1.118] 27.8 [95] [1.200;1.560] 19.3 [67] [1.327;1.460] 14.7 [50] [1.068;1.166] 10.7 [50] [1.166;1.536] 21.7 [95] [0.972;1.501] 19.3 [96] [1.289;1.427] [1.000;1.000] [1.082;1.351] [1.025;1.145] [1.021;1.130] [1.051;1.172] [0.995;1.071] [0.951;1.118] [1.000;1.000] [1.093;1.153] [0.999;1.027] [0.979;1.091] [0.999;1.170] [1.199;1.343] [1.090;1.215] [1.051;1.557] [0.928;1.339] [1.014;1.075]

10 last 16.8 [93] [1.303;1.410] USA first 25 [91] [1.172;1.239] last 25.9 [91] [1.200;1.258] [1.060;1.125] [1.076;1.125] [1.038;1.077] 15.7 [86] [1.247;1.350] 22.4 [78] [1.178;1.242] 23.9 [83] [1.196;1.250] [1.017;1.080] [1.070;1.118] [1.036;1.076] 17.8 [96] [1.290;1.401] 25.7 [94] [1.158;1.227] 27 [95] [1.192;1.253] [1.045;1.101] [1.051;1.090] [1.025;1.057] Sensitivity 1: quadratic b-spline with two internal knots (50 th,90 th ). Sensitivity 2: quadratic b-spline with one internal knot (75 th ). Sensitivity 3: and quadratic b- spline with two internal knots (50 th,95 th ). Lag dimension in all-three analyses was constant (natural spline with two internal knots equally-spaced in the lag dimension, with a maximum lag of 21 days).

11 Table S4. Attributable fraction and 95% confidence interval estimates for cold (mean temperature below the temperature of minimum mortality) per year in each country. YEAR AUSTRALIA BRAZIL CANADA IRELAND JAPAN SOUTH KOREA SPAIN SWITZERLAND UK USA [14.5 ; 20.7] 10.5 [9.6 ; 11.2] 5.6 [5.0 ; 6.1] [4.1 ; 7.1] 17.8 [14.6 ; 20.9] 11.2 [10.4 ; 11.9] 5.5 [5.0 ; 5.9] [3.5 ; 6.6] 15.5 [12.7 ; 18.3] 10.0 [9.2 ; 10.6] 5.4 [4.9 ; 5.8] [11 ; 25.9] 5.7 [4.0 ; 7.2] 13.6 [10.2 ; 16.5] 10.3 [9.5 ; 11.1] 5.8 [5.3 ; 6.3] [11.8 ; 27] 5.8 [4.3 ; 7.1] 12.3 [9.6 ; 15.1] 9.3 [8.5 ; 10.0] 5.8 [5.2 ; 6.2] [10.4 ; 24.2] 5.4 [4.0 ; 6.6] 12.2 [9.1 ; 15.3] 9.1 [8.4 ; 9.8] 6.0 [5.2 ; 6.7] 7.9 [6.8 ; 8.9] 5.3 [4.8 ; 5.7] [10.4 ; 20.0] 5.4 [4.0 ; 6.6] 13.4 [10.7 ; 16.2] 9.5 [8.8 ; 10.1] 7.3 [6.3 ; 8.2] 9.9 [8.7 ; 10.9] 5.5 [5.1 ; 5.8] [12.5 ; 19.6] 5.8 [4.5 ; 6.9] 12.0 [9.2 ; 14.6] 9.5 [8.8 ; 10.1] 8.7 [5.0 ; 12.3] 7.0 [6.1 ; 7.8] 8.8 [7.8 ; 9.7] 5.9 [5.5 ; 6.3] [10.7 ; 17.0] 5.8 [4.6 ; 6.8] 12.0 [9.2 ; 14.6] 10.0 [9.4 ; 10.6] 8.6 [4.8 ; 12] 7.2 [6.4 ; 7.8] 9.5 [8.6 ; 10.4] 6.0 [5.7 ; 6.3] [10.9 ; 16.7] 5.8 [4.7 ; 6.7] 11.7 [9.1 ; 14.2] 9.1 [8.6 ; 9.6] 7.8 [4.8 ; 10.4] 5.4 [4.7 ; 6.0] 8.9 [8.1 ; 9.7] 6.0 [5.6 ; 6.2] [9.5 ; 15.3] 5.6 [4.7 ; 6.5] 10.9 [8.5 ; 13.2] 10.0 [9.4 ; 10.5] 8.6 [5.5 ; 11.4] 4.9 [4.3 ; 5.5] 2.8 [1.5 ; 4.2] 8.5 [7.8 ; 9.2] 6.0 [5.7 ; 6.3] [9.1 ; 14.3] 6.1 [5.1 ; 7.0] 11.9 [9.4 ; 14.3] 10.2 [9.7 ; 10.7] 8.1 [5.5 ; 10.4] 5.4 [4.7 ; 6.1] 3.5 [2.0 ; 4.8] 10.2 [9.6 ; 10.9] 6.6 [6.3 ; 6.9] [8.2 ; 13.2] 4.7 [3.6 ; 5.5] 5.9 [5.1 ; 6.7] 10.3 [7.7 ; 12.6] 9.4 [8.9 ; 9.8] 8.2 [5.9 ; 10.4] 4.5 [3.9 ; 5.1] 2.8 [1.6 ; 3.9] 9.1 [8.5 ; 9.7] 6.4 [6.2 ; 6.7] [6.8 ; 11.3] 3.8 [3.1 ; 4.5] 5.0 [4.4 ; 5.6] 9.8 [7.2 ; 12.1] 8.8 [8.4 ; 9.2] 7.8 [6.0 ; 9.5] 4.8 [4.2 ; 5.5] 2.8 [1.7 ; 3.7] 8.8 [8.4 ; 9.3] 5.8 [5.6 ; 6.1] [6.1 ; 10.3] 4.7 [4.0 ; 5.3] 5.2 [4.6 ; 5.7] 9.9 [7.5 ; 12.3] 9.2 [8.9 ; 9.5] 8.1 [6.4 ; 9.7] 5.6 [5.0 ; 6.1] 2.9 [1.7 ; 4.0] 8.6 [8.2 ; 8.9] 6.3 [6.2 ; 6.5] [5.5 ; 10.0] 4.5 [3.9 ; 5.1] 5.4 [4.8 ; 5.8] 9.8 [6.8 ; 12.7] 9.2 [9.0 ; 9.5] 8.2 [6.4 ; 9.9] 4.9 [4.4 ; 5.4] 1.8 [0.9 ; 2.6] 8.7 [8.3 ; 9.0] 6.4 [6.3 ; 6.6] [4.4 ; 8.5] 3.1 [2.7 ; 3.6] 5.3 [4.8 ; 5.9] 10.1 [7.3 ; 12.9] 9.3 [9.1 ; 9.6] 7.8 [6.4 ; 9.1] 4.2 [3.7 ; 4.6] 1.7 [0.8 ; 2.4] 9.3 [9.0 ; 9.6] 6.4 [6.2 ; 6.5] [3.9 ; 8.0] 2.6 [2.3 ; 3.0] 5.8 [5.1 ; 6.2] 8.8 [5.4 ; 11.9] 8.7 [8.5 ; 8.8] 8.1 [6.6 ; 9.6] 4.2 [3.7 ; 4.6] 1.6 [0.8 ; 2.3] 8.6 [8.3 ; 8.9] 6.5 [6.3 ; 6.7] [2.8 ; 7.9] 3.0 [2.6 ; 3.4] 5.5 [4.9 ; 6.1] 9.0 [5.5 ; 12.4] 9.5 [9.3 ; 9.7] 8.2 [6.7 ; 9.6] 4.1 [3.7 ; 4.5] 2.5 [1.2 ; 3.8] 8.8 [8.5 ; 9.1] 6.7 [6.6 ; 6.9] [1.8 ; 6.5] 3.4 [3.0 ; 3.8] 5.2 [4.6 ; 5.7] 9.0 [5.1 ; 12.2] 8.5 [8.3 ; 8.7] 7.9 [6.5 ; 9.2] 3.9 [3.4 ; 4.3] 2.2 [0.6 ; 3.7] 8.8 [8.5 ; 9.2] 6.6 [6.4 ; 6.8] [0.5 ; 5.8] 2.4 [2.0 ; 2.7] 5.3 [4.8 ; 5.8] 8.8 [4.7 ; 12.1] 9.4 [9.1 ; 9.6] 8.3 [6.5 ; 9.9] 5.1 [4.5 ; 5.5] 3.3 [1.5 ; 5.0] 9.1 [8.7 ; 9.4] 6.7 [6.5 ; 6.8] [-0.4 ; 5.6] 2.8 [2.3 ; 3.1] 5.1 [4.5 ; 5.7] 8.7 [4.8 ; 12.3] 9.2 [8.9 ; 9.5] 8.1 [6.2 ; 9.9] 3.8 [3.3 ; 4.3] 3.0 [1.2 ; 4.6] 8.8 [8.4 ; 9.2] 6.6 [6.4 ; 6.8] [-1.8 ; 5.2] 2.6 [1.8 ; 3.2] 5.3 [4.5 ; 6.0] 8.2 [3.6 ; 12.1] 8.2 [7.8 ; 8.6] 7.8 [5.7 ; 9.7] 3.6 [2.9 ; 4.4] 2.3 [0.1 ; 4.5] 8.6 [8.0; 9.1] [-3.1 ; 4.7] 2.9 [2.1 ; 3.7] 5.5 [4.8 ; 6.2] 9.2 [8.7 ; 9.6] 8.3 [5.9 ; 10.3] 3.4 [2.6 ; 4.2] 3.0 [0.3 ; 5.6] 9.4 [8.8 ; 10.0] [1.3 ; 3.3] 5.8 [4.8 ; 6.6] 8.6 [8.1 ; 9.0] 8.1 [5.5 ; 10.2] 3.5 [2.7 ; 4.2] 3.6 [0.7 ; 6.0] 9.4 [8.9 ; 10.0] [1.4 ; 3.0] 5.8 [4.9 ; 6.8] 8.8 [8.2 ; 9.3] 8.7 [6.0 ; 11.1] 3.7 [2.9 ; 4.5] 4.5 [1.2 ; 7.4] 11.2 [10.6 ; 11.8] [1.9 ; 3.8] 6.2 [5 ; 7.3] 9.6 [8.9 ; 10.1] 3.8 [0.2 ; 6.7] 8.8 [8.1 ; 9.5] [9.4 ; 10.4] 4.7 [1.1 ; 8.1]

12 Table S5. Observed attributable fraction and 95% confidence interval estimates for heat (mean temperature above the temperature of minimum mortality) per year in each country. YEAR AUSTRALIA BRAZIL CANADA IRELAND JAPAN SOUTH KOREA SPAIN SWITZERLAND UK USA [-0.02 ; 0.03] 0.81 [0.74 ; 0.88] 0.30 [0.26 ; 0.33] [0.34 ; 0.58] 0.03 [-0.02 ; 0.08] 0.36 [0.32 ; 0.40] 0.32 [0.28 ; 0.35] [0.60 ; 0.91] 0.03 [-0.04 ; 0.10] 0.52 [0.46 ; 0.57] 0.52 [0.47 ; 0.57] [-0.06 ; 0.02] 1.01 [0.81 ; 1.19] 0.00 [0.00 ; 0.01] 0.23 [0.20 ; 0.25] 0.80 [0.72 ; 0.86] [-0.01 ; 0.00] 0.54 [0.43 ; 0.64] 0.11 [-0.07 ; 0.27] 0.32 [0.28 ; 0.35] 0.32 [0.28 ; 0.34] [-0.02 ; 0.01] 0.47 [0.37 ; 0.57] 0.06 [-0.04 ; 0.17] 0.91 [0.82 ; 0.99] 1.46 [1.09 ; 1.80] 0.53 [0.43 ; 0.62] 0.35 [0.30 ; 0.38] [-0.17 ; 0.17] 0.68 [0.54 ; 0.81] 0.04 [-0.04 ; 0.12] 0.48 [0.43 ; 0.53] 1.70 [1.39 ; 1.98] 0.19 [0.14 ; 0.24] 0.55 [0.50 ; 0.6] [-0.10 ; 0.14] 0.16 [0.12 ; 0.20] 0.01 [-0.01 ; 0.02] 0.44 [0.39 ; 0.48] 0.16 [0.06 ; 0.25] 1.14 [0.88 ; 1.38] 0.09 [0.07 ; 0.11] 0.18 [0.16 ; 0.20] [-0.17 ; 0.28] 0.41 [0.31 ; 0.50] 0.00 [0.00 ; 0.00] 0.07 [0.06 ; 0.08] 0.00 [0.00 ; 0.01] 0.97 [0.75 ; 1.17] 0.04 [0.03 ; 0.05] 0.47 [0.43 ; 0.51] [-0.08 ; 0.31] 0.40 [0.32 ; 0.48] 0.00 [-0.01 ; 0.01] 1.25 [1.15 ; 1.35] 1.42 [0.79 ; 1.98] 1.69 [1.40 ; 1.94] 0.28 [0.22 ; 0.33] 0.43 [0.39 ; 0.46] [-0.02 ; 0.24] 0.65 [0.52 ; 0.76] 0.11 [-0.16 ; 0.38] 0.74 [0.67 ; 0.81] 0.36 [0.18 ; 0.52] 1.26 [1.01 ; 1.51] 2.14 [1.05 ; 3.14] 0.98 [0.84 ; 1.13] 0.56 [0.51 ; 0.61] [0.01 ; 0.21] 0.26 [0.20 ; 0.31] 0.00 [-0.01 ; 0.02] 0.40 [0.36 ; 0.44] 0.40 [0.21 ; 0.58] 0.60 [0.56 ; 0.65] 1.41 [0.46 ; 2.23] 0.20 [0.17 ; 0.23] 0.20 [0.17 ; 0.22] [0.06 ; 0.58] 0.43 [0.28 ; 0.58] 0.35 [0.28 ; 0.41] 0.02 [-0.05 ; 0.09] 0.29 [0.26 ; 0.32] 0.46 [0.28 ; 0.66] 0.59 [0.55 ; 0.63] 1.57 [0.58 ; 2.57] 0.50 [0.43 ; 0.58] 0.26 [0.23 ; 0.29] [0.22 ; 0.75] 1.34 [1.02 ; 1.63] 0.55 [0.44 ; 0.66] 0.00 [-0.01 ; 0.01] 0.37 [0.32 ; 0.41] 0.14 [0.08 ; 0.21] 1.11 [1.04 ; 1.19] 1.87 [0.99 ; 2.69] 0.10 [0.08 ; 0.11] 0.35 [0.31 ; 0.39] [0.10 ; 0.39] 0.56 [0.41 ; 0.69] 0.64 [0.47 ; 0.78] 0.00 [-0.05 ; 0.06] 0.44 [0.39 ; 0.49] 0.31 [0.17 ; 0.44] 0.94 [0.88 ; 0.99] 1.33 [0.53 ; 2.18] 0.32 [0.27 ; 0.36] 0.44 [0.39 ; 0.47] [0.17 ; 0.49] 0.34 [0.25 ; 0.42] 0.23 [0.17 ; 0.28] 0.00 [-0.01 ; 0.01] 0.45 [0.39 ; 0.50] 0.32 [0.17 ; 0.46] 0.71 [0.67 ; 0.75] 1.26 [0.50 ; 2.01] 0.15 [0.13 ; 0.17] 0.20 [0.17 ; 0.22] [0.31 ; 0.78] 0.50 [0.39 ; 0.62] 0.54 [0.41 ; 0.65] 0.00 [-0.02 ; 0.02] 0.39 [0.35 ; 0.44] 0.31 [0.15 ; 0.47] 0.88 [0.83 ; 0.94] 1.19 [0.43 ; 1.86] 0.37 [0.31 ; 0.41] 0.29 [0.26 ; 0.32] [0.27 ; 0.56] 0.66 [0.51 ; 0.79] 0.70 [0.54 ; 0.87] 0.00 [0.00 ; 0.00] 0.41 [0.36 ; 0.46] 0.14 [0.07 ; 0.21] 0.49 [0.45 ; 0.52] 0.98 [0.38 ; 1.56] 0.17 [0.14 ; 0.20] 0.42 [0.37 ; 0.47] [0.25 ; 0.56] 0.76 [0.60 ; 0.89] 0.42 [0.32 ; 0.52] [-0.08 ; 0.03] 0.13 [0.11 ; 0.16] 0.03 [0.01 ; 0.05] 2.38 [2.23 ; 2.51] 2.60 [1.82 ; 3.34] 0.64 [0.55 ; 0.72] 0.23 [0.19 ; 0.26] [0.62 ; 1.16] 0.37 [0.29 ; 0.44] 0.26 [0.19 ; 0.35] 0.00 [-0.01 ; 0.00] 0.33 [0.28 ; 0.38] 0.30 [0.15 ; 0.44] 1.14 [1.06 ; 1.22] 0.59 [0.23 ; 0.91] 0.29 [0.24 ; 0.34] 0.15 [0.12 ; 0.17] [0.33 ; 0.70] 0.81 [0.67 ; 0.96] 0.62 [0.38 ; 0.83] [-0.03 ; 0.00] 0.20 [0.16 ; 0.23] 0.19 [0.06 ; 0.32] 1.09 [1.00 ; 1.17] 0.71 [0.40 ; 1.00] 0.30 [0.25 ; 0.34] 0.37 [0.32 ; 0.42] [0.58 ; 1.17] 0.69 [0.53 ; 0.85] 0.47 [0.26 ; 0.65] [-0.14 ; 0.02] 0.17 [0.14 ; 0.21] 0.24 [0.06 ; 0.40] 1.33 [1.21 ; 1.43] 1.00 [0.54 ; 1.41] 0.75 [0.65 ; 0.86] 0.36 [0.30 ; 0.41] [0.44 ; 0.94] 0.69 [0.48 ; 0.89] 0.41 [0.22 ; 0.58] 0.00 [0.00 ; 0.00] 0.21 [0.16 ; 0.25] 0.17 [0.01 ; 0.30] 0.52 [0.47 ; 0.56] 0.28 [0.14 ; 0.41] 0.03 [0.02 ; 0.04] [0.35 ; 0.78] 0.53 [0.38 ; 0.68] 0.22 [0.10 ; 0.35] 0.13 [0.09 ; 0.17] 0.16 [0.03 ; 0.29] 0.59 [0.52 ; 0.65] 0.32 [0.15 ; 0.49] 0.12 [0.09 ; 0.15] [0.46 ; 0.85] 0.16 [0.05 ; 0.25] 0.03 [0.02 ; 0.05] 0.08 [-0.01 ; 0.16] 1.14 [1.01 ; 1.25] 0.37 [0.14 ; 0.58] 0.19 [0.15 ; 0.23] [0.82 ; 1.43] 0.26 [0.09 ; 0.43] 0.26 [0.17 ; 0.34] 0.28 [-0.04 ; 0.57] 1.02 [0.90 ; 1.13] 0.39 [0.13 ; 0.63] 0.14 [0.10 ; 0.18] [0.53 ; 1.10] 0.24 [0.05 ; 0.39] 0.12 [0.07 ; 0.17] 0.25 [0.05 ; 0.43] 0.13 [0.10 ; 0.16] [0.06 ; 0.15] 0.24 [-0.01 ; 0.46]

13 Figure S1. Daily mean temperature distribution estimated in the first and last year available in each country. Point-dashed and dashed lines correspond to the median value estimated in the first and last year, respectively. Distribution was estimated on the average daily series across locations in each country. Figure S2. Overall cumulative temperature-mortality associations (relative risk (RR)) predicted for the first (grey) and last (black) years of each series, and the average exposure-response curve estimate across the whole series (red) in each country. The curves are represented on a relative scale of temperature percentiles, using average country-specific distributions, and re-centered in the corresponding temperature of minimum mortality in each year. Figure S3. Effect modification of time on the overall cumulative exposure-response relationships between temperature and mortality, expressed as ratio of relative risk (RRR) and 95% confidence interval. The vertical line represents the percentile of minimum mortality temperature of the overall cumulative exposure response curve from the model without interaction. Figure S4. Temporal trends in cold-attributable mortality in each country, reported in terms of yearly fractions (%) and 95% confidence intervals (temperatures below the temperature of minimum mortality). Figure S5. Temporal trends in heat-attributable mortality in each country, reported in terms of yearly fractions (%) and 95% confidence intervals (temperatures above the temperature of minimum mortality). Figure S6. Observed and predicted cold-attributable fractions (%) per 5-year period assuming a constant temperature distribution and a constant exposure-response relationship in each country (temperatures below the temperature of minimum mortality). The y-axis is scaled to the country-specific range. Figure S7. Observed and predicted heat-attributable fractions (%) per 5-year period assuming a constant temperature distribution and a constant exposure-response relationship in each country (temperatures above the temperature of minimum mortality). The y-axis is scaled to the country-specific range.

14 Methods S1. Selection of the cross-basis specifications. We tested different combinations of non-linear functions in the two dimensions of the cross-basis of the exposure variable. The final definition used in the main analysis of the present study would be the one reporting the lowest q-aic. Specifically, in the exposure-response dimension, we tested between cubic natural spline and quadratic b- spline with different number of internal knots placed in specific percentiles of the exposure variable (mean temperature) in each location (5 th, 10 th, 25 th, 50 th,75 th, 90 th, 95 th ). However, we kept constant the definition of function in the lag dimension (natural spline with two internal knots equally-spaced in the log scale) with a maximum lag of 21 days. We took that decision because we were not interested in exploring the shape in the present analysis. We just wanted to properly model this dimension using a simple nonfunction, chosen based on previous studies (Gasparrini Lancet 2015), so the resulting cross-basis would not be very complex to be used in the interaction model. In table S3 of this appendix, we show the results obtained using the three combinations of cross-basis specifications with a lowest qaic, above the one selected for the main analysis of the present study.