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The productivity of important agricultural crops is drastically reduced when they experience short episodes of high temperatures during the reproductive period. Crop heat stress was acknowledged in the IPCC 4th Assessment Report as an important threat to global food supply. We produce a first spatial assessment of heat stress risk at a global level for four key crops, wheat, maize, rice and soybean, using the FAO/IIASA Global Agro-Ecological Zones Model (GAEZ). A high risk of yield damage was found for continental lands at high latitudes, particularly in the Northern Hemisphere between 40 and 60°N. Central and Eastern Asia, Central North America and the Northern part of the Indian subcontinent have large suitable cropping areas under heat stress risk. Globally, this ranged from less than 5 Mha of suitable lands for maize for the baseline climate (1971–2000) to more than 120 Mha for wetland rice for a future climate change condition (2071–2100) assuming the A1B emission scenario. For most crops and regions, the intensity, frequency and relative damage due to heat stress increased from the baseline to the A1B scenario. However for wheat and rice crops, GAEZ selection of different crop types and sowing dates in response to A1B seasonal climate caused a reduction in heat stress impacts in some regions, which suggests that adaptive measures considering these management options may partially mitigate heat stress at local level. Our results indicate that temperate and sub-tropical agricultural areas might bear substantial crop yield losses due to extreme temperature episodes and they highlight the need to develop adaptation strategies and agricultural policies able to mitigate heat stress impacts on global food supply.