This paper argues that extreme heat stress during the crop reproductive period can be critical for crop productivity. Projected changes in the frequency and severity of extreme climatic events are expected to negatively impact crop yields and global food production. This study applies the global crop model PEGASUS to quantify, at the global scale, impacts of extreme heat stress on maize, spring wheat and soybean yields resulting from 72 climate change scenarios for the 21st century. The results project maize to face progressively worse impacts under a range of RCPs but spring wheat and soybean to improve globally through to the 2080s due to CO2 fertilization effects, even though parts of the tropic and sub-tropic regions could face substantial yield declines.