Mortality due to extreme temperatures is one of the most worrying impacts of climate change. In this analysis, we use historic mortality and temperature data from 106 cities in the United States to develop a model that predicts deaths attributable to temperature. With this model and projections of future temperature from climate models, we estimate temperature‐related deaths in the United States due to climate change, changing demographics, and adaptation. We find that temperature‐related deaths increase rapidly as the climate warms, but this is mainly due to an expanding and aging population. For global average warming below 3°C above pre‐industrial levels, we find that climate change slightly reduces temperature‐related mortality in the U.S. because the reduction of cold‐related mortality exceeds the increase in heat‐related deaths. Above 3°C warming, whether the increase in heat‐related deaths exceeds the decrease in cold‐related deaths depends on the level of adaptation. Southern U.S. cities are already well adapted to hot temperatures and the reduction of cold‐related mortality drives overall lower mortality. Cities in the Northern U.S. are not well adapted to high temperatures, so the increase in heat‐related mortality exceeds the reduction in cold‐related mortality. Thus, while the total number of climate‐related mortality may not change much, climate change will shift mortality in the U.S. to higher latitudes.