Stresses from heat and drought are expected to increasingly suppress crop yields, but the degree to which current models can represent these effects is uncertain. Here we evaluate the algorithms that determine impacts of heat and drought stress on maize in 16 major maize models by incorporating these algorithms into a standard model, the Agricultural Production Systems sIMulator (APSIM), and running an ensemble of simulations. Although both daily mean temperature and daylight temperature are common choice of forcing heat stress algorithms, current parameterizations in most models favor the use of daylight temperature even though the algorithm was designed for daily mean temperature. Different drought algorithms (i.e., a function of soil water content, of soil water supply to demand ratio, and of actual to potential transpiration ratio) simulated considerably different patterns of water shortage over the growing season, but nonetheless predicted similar decreases in annual yield. Using the selected combination of algorithms, our simulations show that maize yield reduction was more sensitive to drought stress than to heat stress for the US Midwest since the 1980s, and this pattern will continue under future scenarios; the influence of excessive heat will become increasingly prominent by the late 21st century. Our review of algorithms in 16 crop models suggests that the impacts of heat and drought stress on plant yield can be best described by crop models that: (i) incorporate event-based descriptions of heat and drought stress, (ii) consider the effects of nighttime warming, and (iii) coordinate the interactions among multiple stresses. Our study identifies the proficiency with which different model formulations capture the impacts of heat and drought stress on maize biomass and yield production. The framework presented here can be applied to other modeled processes and used to improve yield predictions of other crops with a wide variety of crop models.