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We estimate how the mortality effects of temperature vary across U.S. climate regions to assess local and national damages from projected climate change. Using 22 years of Medicare data, we find that both cold and hot days increase mortality. However, hot days are less deadly in warm places while cold days are less deadly in cool places. Incorporating this heterogeneity into end-of-century climate change assessments reverses the conventional wisdom on climate damage incidence: cold places bear more, not less, of the mortality burden. Allowing places to adapt to their future climate substantially reduces the estimated mortality effects of climate change.