We study potential impacts of future climate change on U.S. agricultural productivity using county‐level yield and weather data from 1950 to 2015. To account for adaptation of production to different weather conditions, it is crucial to allow for both spatial and temporal variation in the production process mapping weather to crop yields. We present a new panel data estimation technique, called mean observation OLS (MO‐OLS) that allows for spatial and temporal heterogeneity in all regression parameters (intercepts and slopes). Both forms of heterogeneity are important: We find strong evidence that production function parameters adapt to local climate, and also that sensitivity of yield to high temperature declined from 1950–89. We use our estimates to project corn yields to 2100 using 19 climate models and three greenhouse gas emission scenarios. We predict unmitigated climate change will greatly reduce yield. Our mean prediction (over climate models) is that adaptation alone can mitigate 36% of the damage, while emissions reductions consistent with the Paris targets would mitigate 76%.