Asseng, S. et al. Crop models are essential tools for assessing the threat of climate change to local and global food production1. Present models used to predict wheat grain yield are highly uncertain when simulating how crops respond to temperature2. 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. We thank the Agricultural Model Intercomparison and Improvement Project and its leaders C. Rosenzweig from NASA Goddard Institute for Space Studies and Columbia University (USA), J. Jones from University of Florida (USA), J. Hatfield from United States Department of Agriculture (USA) and J. Antle from Oregon State University (USA) for support. We also thank M. Lopez from CIMMYT (Turkey), M. Usman Bashir from University of Agriculture, Faisalabad (Pakistan), S. Soufizadeh from Shahid Beheshti University (Iran), and J. Lorgeou and J-C. Deswarte from ARVALIS—Institut du Végétal (France) for assistance with selecting key locations and quantifying regional crop cultivars, anthesis and maturity dates and R. Raymundo for assistance with GIS. S.A. and D.C. received financial support from the International Food Policy Research Institute (IFPRI). C.S. was funded through USDA National Institute for Food and Agriculture award 32011-68002-30191. C.M. received financial support from the KULUNDA project (01LL0905L) and the FACCE MACSUR project (031A103B) funded through the German Federal Ministry of Education and Research (BMBF). F.E. received support from the FACCE MACSUR project (031A103B) funded through the German Federal Ministry of Education and Research (2812ERA115) and E.E.R. was funded through the German Science Foundation (project EW 119/5-1). M.J. and J.E.O. were funded through the FACCE MACSUR project by the Danish Strategic Research Council. K.C.K. and C.N. were funded by the FACCE MACSUR project through the German Federal Ministry of Food and Agriculture (BMEL). F.T., T.P. and R.P.R. received financial support from FACCE MACSUR project funded through the Finnish Ministry of Agriculture and Forestry (MMM); F.T. was also funded through National Natural Science Foundation of China (No. 41071030). C.B. was funded through the Helmholtz project ‘REKLIM—Regional Climate Change: Causes and Effects’ Topic 9: ‘Climate Change and Air Quality’. M.P.R. and P.D.A. received funding from the CGIAR Research Program on Climate Change, Agriculture, and Food Security (CCAFS). G.O’L. was funded through the Australian Grains Research and Development Corporation and the Department of Environment and Primary Industries Victoria, Australia. R.C.I. was funded by Texas AgriLife Research, Texas A&M University. E.W. and Z.Z. were funded by CSIRO and the Chinese Academy of Sciences (CAS) through the research project ‘Advancing crop yield while reducing the use of water and nitrogen’ and by the CSIRO-MoE PhD Research Program. Peer reviewed