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. The model ensemble median was consistently more accurate in simulating the crop temperature response than any single model, regardless of the input information used. Extrapolating the model ensemble temperature response indicates that warming is already slowing yield gains at a majority of wheat-growing locations. Global wheat production is estimated to fall by 6% for each ?C of further temperature increase and become more variable over space and time.