There is widespread interest in the impacts of climate change on agriculture in Sub-Saharan Africa (SSA), and on the most effective investments to assist adaptation to these changes, yet the scientific basis for estimating production risks and prioritizing investments has been quite limited. Here we show that by combining historical crop production and weather data into a panel analysis, a robust model of yield response to climate change emerges for several key African crops. By mid-century, the mean estimates of aggregate production changes in SSA under our preferred model specification are - 22, - 17, - 17, - 18, and - 8% for maize, sorghum, millet, groundnut, and cassava, respectively. In all cases except cassava, there is a 95% probability that damages exceed 7%, and a 5% probability that they exceed 27%. Moreover, countries with the highest average yields have the largest projected yield losses, suggesting that well-fertilized modern seed varieties are more susceptible to heat related losses.