Statistical studies of rainfed maize yields in the United States and elsewhere have indicated two clear features: a strong negative yield response to accumulation of temperatures above 30 °C (or extreme degree days (EDD)), and a relatively weak response to seasonal rainfall. Here we show that the process-based Agricultural Production Systems Simulator (APSIM) is able to reproduce both of these relationships in the Midwestern United States and provide insight into underlying mechanisms. The predominant effects of EDD in APSIM are associated with increased vapour pressure deficit, which contributes to water stress in two ways: by increasing demand for soil water to sustain a given rate of carbon assimilation, and by reducing future supply of soil water by raising transpiration rates. APSIM computes daily water stress as the ratio of water supply to demand, and during the critical month of July this ratio is three times more responsive to 2 °C warming than to a 20% precipitation reduction. The results suggest a relatively minor role for direct heat stress on reproductive organs at present temperatures in this region. Effects of elevated CO2 on transpiration efficiency should reduce yield sensitivity to EDD in the coming decades, but at most by 25%.