Rising air temperatures are a leading risk to global crop production. Recent research has emphasized the critical role of moisture availability in regulating crop responses to heat and the importance of temperature–moisture couplings in driving concurrent heat and drought. Here, we demonstrate that the heat sensitivity of key global crops depends on the local strength of couplings between temperature and moisture in the climate system. Over 1970–2013, maize and soy yields dropped more during hotter growing seasons in places where decreased precipitation and evapotranspiration more strongly accompanied higher temperatures, suggestive of compound heat–drought impacts on crops. On the basis of this historical pattern and a suite of climate model projections, we show that changes in temperature–moisture couplings in response to warming could enhance the heat sensitivity of these crops as temperatures rise, worsening the impact of warming by −5% (−17 to 11% across climate models) on global average. However, these changes will benefit crops where couplings weaken, including much of Asia, and projected impacts are highly uncertain in some regions. Our results demonstrate that climate change will impact crops not only through warming but also through changing drivers of compound heat–moisture stresses, which may alter the sensitivity of crop yields to heat as warming proceeds. Robust adaptation of cropping systems will need to consider this underappreciated risk to food production from climate change.