Nitrogen and water supply modulate the effect of elevated temperature on wheat yield

•Yield gaps for temperature-limited yield potential YT varied with location, time of sowing, cultivar and nitrogen.•YT related negatively to mean temperature in the critical period returning a slope of -0.53 t ha−1 °C−1.•Elevated temperature reduced the duration of the critical period and was the largest driver of reduced grain number and yield.•Yield-temperature relationships crossed over in the response to nitrogen fertilisation. Elevated temperature, water deficit, low nitrogen availability and their interactions, constrain wheat yield in Mediterranean-type environments. Our working hypothesis is that, owing to the non-linearity of yield response to water and nitrogen and the non-linearity of biological processes in response to temperature, the outcome of the interactions between temperature, nitrogen and water is range-dependent. To generate a broad range of conditions in testing this hypothesis, we established two experiments. Experiment 1 combined factorially four sowing times, six cultivars and four nitrogen rates in four locations-seasons. Experiment 2 combined factorially two cultivars, two nitrogen rates, and two thermal regimes to further untangle interactions. Thermal regimes were unheated controls, and crops heated with passive open-top heating chambers increasing temperature by 0.5 °C during grain set or grain filling. Across the 384 combinations of treatments in Experiment 1, yield ranged between 0.12 t ha-1 and 5.96 t ha-1. The duration of the critical period (300 °C d before anthesis to 100 °C d after anthesis) decreased with mean temperature at an average rate of 5 d °C-1 and accounted for 75% of the variation in yield. We used quantile regression to calculate a temperature-limited yield potential YT and derived a linear function between YT and mean temperature in the critical period, returning a slope of -0.53 t ha-1 °C-1. Yield gap, i.e., the difference between YT and actual yield, was larger in nitrogen and water-deficient crops. Yield-temperature relationships crossed over in response to nitrogen fertilisation. Fertilised crops (100−200 kg N ha-1) outyielded their unfertilised counterparts when mean temperature during the critical period was below 13 °C, and unfertilised controls were superior above this threshold. Locally calibrated thresholds can be used as a rule-of-thumb adding a further dimension to the management of combined stresses and risk of wheat in Mediterranean-type environments. In Experiment 2, yield responded to the in