Crop yields are determined by multiple process chains that respond to environmental conditions. The very complex interactions between the different processes as well as the effects of isolated and combined process-level signals on final yields can be examined with process-based models. One of the key signals for crop development and growth dynamics is temperature, which is subject to change under global warming. While some crop models compute temperatures at the canopy level, others take 2 m air temperatures as input. However, the two temperatures can deviate significantly, potentially leading to different process responses when the less accurate 2 m air temperatures are used. This particularly applies to high-temperature processes that exhibit nonlinear dynamics and are very sensitive to small temperature variations. For global models, a major limitation is the computational resources required by suitable canopy temperature approaches. In this study we present computationally efficient emulators based on a complex energy balance approach (EBSC) to simulate daily mean and maximum canopy temperatures of twelve different crops. The emulators are statistical models that include six variables describing weather conditions and crop status. Furthermore, the emulators contain interaction terms to consider the response of canopy temperature on interactions between the variables. We apply and evaluate the emulators in the global, process-based Lund-Potsdam-Jena managed Land (LPJmL) model and show that the emulator approach reproduces observed canopy heating and cooling effects depending on the water and nitrogen status of wheat. Furthermore, we compare the simulated daily mean and daily maximum canopy temperatures of all twelve crops to a global dataset of ERA5 skin temperatures. We find that, for daily mean temperatures, 2 m air temperatures are the better approximation of skin temperatures than the simulated canopy temperatures, whereas for daily maximum temperatures simulated canopy temperatures consistently outperform 2 m air temperatures in terms of bias and nonunity slope. Our results indicate that heat effects are substantially underestimated with 2 m air temperatures, while they are significantly better captured with simulated canopy temperatures. This suggests that replacing the 2 m air temperature input by simulated canopy temperatures considerably improves the ability to model high temperature impacts on crop growth.