Abstract: To deliver food security for the 9 billon population in 2050, a 70% increase in world food supply will be required. Predicted climate change emphasises the need for breeding strategies that delivers both a substantial increase in yield potential and resilience to extreme weather events such as heat waves, late frost or severe drought. Heat stress around sensitive stages of wheat development has been identified as a possible threat to wheat production in Europe. However, no estimates have been made to assess yield losses due to increased frequency and magnitude of heat stress under climate change. Using existing experimental data, we refined the Sirius wheat model and incorporated effects of extreme temperature during flowering and grain filling on accelerated leaf senescence, grain number and grain weight. This allowed us, for the first time, to quantify yield losses resulting from heat stress under climate change. We used Sirius to design wheat ideotypes optimised for CMIP5-based climate scenarios for 2050 at 6 wheat growing areas in Europe. The yield potential for heat-tolerant ideotypes can be substantially increased compared with the current cultivars in the future by selecting optimal combination of wheat traits, e.g. optimal phenology and extended duration of grain filling. However, grain yield of heat-sensitive ideotypes was substantially lower and more variable in Hungary and Spain, because extending grain filling for increased yield potential was in conflict with high temperature episodes during flowering and grain filling. Despite much earlier flowering at these sites, the risk of heat stress affecting yields of heat-sensitive ideotypes remained high. Therefore, heat tolerance in wheat is likely to become a key trait for increased yield potential and yield stability in southern Europe in the future. No Label