Climate change is rapidly deteriorating environmental conditions around the world through drought and floods, powerful hurricanes, wildfires, rising temperatures, and more frequent and longer heatwaves. A growing literature has now documented that higher temperatures have already contributed to increasing mortality risks in most of the world. A central question is therefore how will societies adapt to climate change and what are the costs of adaptation? This paper begins by presenting new evidence on the benefits of health adaptation to extreme heat by documenting the temporal evolution of heat-related mortality in the United States using county-level data. The paper then reports the first evidence that compares the private and external costs of climate change adaptation through electricity usage, which powers most cooling technologies such as air-conditioning. A key finding is that the external costs of adaptation that arise through higher electricity consumption (i.e., increased emissions of health-damaging air pollutants and carbon) are more than twice as large as the private costs (i.e., increased residential expenditures on electricity). These findings further underscore the importance of quickly decarbonizing the electricity sector.