Crop models are essential tools for assessing the threat of climate change to local and global food production. Present models used to predict wheat grain yield are highly uncertain when simulating how crops respond to temperature. Here we systematically tested 30 different wheat crop models of the Agricultural Model Intercomparison and Improvement Project against field experiments in which growing season mean temperatures ranged from 15 °C to 32 °C, including experiments with artificial heating. Many models simulated yields well, but were less accurate at higher temperatures.