This dataset comprises the output data of simulations carried out by nine different crop modelling groups for grain maize and winter wheat over the EU-27. Five models simulated both maize and wheat (4M; FASSET, FA, HERMES, HE, MONICA, MO and SIMPLACE-Lintul5, L5), three models simulated only winter wheat (SIRIUS 2015, S2; SiriusQuality v3, SQ) and IXIM, IX simulated only grain maize. All models included a heat stress response that reduces the final yield under high temperatures, mechanisms to reduce growth and leaf area under water limitation, and account for the effects of CO2 on either radiation use efficiency (RUE) or photosynthesis. Five of the models include algorithms to estimate crop canopy temperature (FA, L5, HE, SS, S2). All models, except for sQ and S2 also include the effects of CO2 on reducing transpiration. Simulations were conducted for combinations of three representative concentration pathways (RCPs) and five general circulation models (GCMs). Time periods considered were 2040-2069 and 2070-2099 for the projection scenarios, and years 1980-2010 for a historical period. Parts of this dataset were used as the basis for analyzing crop responses to climate, as described in Webber et al. 2018. Other key details and a more extensive description of each model's consideration of heat and drought stress are listed in the supplementary materials of Webber et al. 2018.