Heat and water stress can drastically reduce crop yields, particularly when they co-occur, but their combined effects and the mitigating potential of irrigation have not been simultaneously assessed at the regional scale. We quantified the combined effects of temperature and precipitation on county-level maize and soybean yields from irrigated and rainfed cropping in the USA in 1970–2010, and estimated the yield changes due to expected future changes in temperature and precipitation. We hypothesized that yield reductions would be induced jointly by water and heat stress during the growing season, caused by low total precipitation (P_GS) and high mean temperatures (T_GS) over the whole growing season, or by many consecutive dry days (CDD_GS) and high mean temperature during such dry spells (T_CDD) within the season. Whole growing season (T_GS, P_GS) and intra-seasonal climatic indices (T_CDD, CDD_GS) had comparable explanatory power. Rainfed maize and soybean yielded least under warm and dry conditions over the season, and with longer dry spells and higher dry spell temperature. Yields were lost faster by warming under dry conditions, and by lengthening dry spells under warm conditions. For whole season climatic indices, maize yield loss per degree increase in temperature was larger in wet compared with dry conditions, and the benefit of increased precipitation greater under cooler conditions. The reverse was true for soybean. An increase of 2 °C in T_GS and no change in precipitation gave a predicted mean yield reduction across counties of 15.2% for maize and 27.6% for soybean. Irrigation alleviated both water and heat stresses, in maize even reverting the response to changes in temperature, but dependencies on temperature and precipitation remained. We provide carefully parameterized statistical models including interaction terms between temperature and precipitation to improve predictions of climate change effects on crop yield and context-dependent benefits of irrigation.