Stable and sufficient food supplies are increasingly threatened by climatic variability, in particular extreme heat events. Intraspecific crop diversity may be an important biological resource to both understand and maintain crop resilience to extreme conditions. Here using data from a mass field experiment screening for heat tolerance in sweet potato (Ipomoea batatas), we identify 132 heat-tolerant cultivars and breeding lines (6.7%) out of 1,973 investigated. Sweet potato is the world's fifth most important food crop, and mean conditions experienced by sweet potato by 2070 are predicted to be 1 to 6 °C warmer, negatively impacting most genotypes. We identify canopy temperature depression, chlorophyll content and storage root-flesh colour as predictors of heat tolerance and, therefore, as potential traits for breeding consideration. These results highlight the role of intraspecific biodiversity for the productivity and resilience of food and agricultural systems in the face of climate change.