Mounting evidence suggests that even brief periods of high temperatures occurring around flowering and during grain filling can produce very large grain yield losses in cereals, a phenomenon referred to as heat stress. Very recently, crop models have started to account for such phenomenon. Most use air temperature (Tair) in their heat stress responses despite evidence that crop canopy temperature (Tc) better explains yield losses. Tc can deviate significantly from Tair based on climatic factors and the crop water status. The broad objective of this study was to evaluate if simulation and use of Tc improves crop models’ ability to simulate heat stress impacts on wheat under irrigated conditions. Nine process-based crop models, each using one of three broad approaches (empirical, EMP, energy balance assuming neutral atmospheric stability, EBN, and energy balance correcting for the atmospheric stability conditions, EBSC) to simulate Tc, simulated grain yield under a range of temperature conditions. The models varied widely in their ability to reproduce the observed Tc with the commonly used EBN models performing much worse than either EMP or EBSC. Use of Tc to account for heat stress effects did improve simulations compared to using only Tair to a relatively minor extent, but use of Tc on more processes did not result in better yield simulations. Models that did well in simulating yield under heat stress had varying skill in simulating Tc, highlighting the need to more systematically understand and model heat stress events in wheat.