Will climate change worsen U.S. inequality? Focusing on the case of extreme temperatures in the U.S., this paper develops an Aiyagari-style heterogeneous agent model to study the distributional impacts of climate change across income groups. Households can adapt to extreme temperatures by using capital and energy for heating and cooling. The model replicates empirical relationships between energy budget shares, energy expenditures, and income. A key insight from the model is that the outdoor temperature acts as a transfer from nature to households. Extreme temperatures correspond to reductions in transfers from nature and thus have higher welfare cost for lower income households. Consequently, climate change is generally regressive in hot regions of the U.S., where it leads to more extreme temperatures and progressive in cold regions, where it leads to fewer extreme temperatures. Households in the lowest income deciles break this pattern because climate change affects whether these households purchase both heating and cooling capital or can specialize in a single type of energy capital.