High temperature and drought stress are projected to reduce crop yields and threaten food security. While effects of heat and drought on crop growth and yield have been studied separately, little is known about the combined effect of these stressors. We studied detrimental effects of high temperature, drought stress and combined heat and drought stress around anthesis on yield and its components for three wheat cultivars originating from Germany and Iran. We found that effects of combined heat and drought on the studied physiological and yield traits were considerably stronger than those of the individual stress factors alone, but the magnitude of the effects varied for specific growth‐ and yield‐related traits. Single grain weight was reduced under drought stress by 13%–27% and under combined heat and drought stress by 43%–83% but not by heat stress alone. Heat stress significantly decreased grain number by 14%–28%, grain yield by 16%–25% and straw yield by 15%–25%. Cultivar responses were similar for heat but different for drought and combined heat and drought treatments. We conclude that heat stress as imposed in this study is less detrimental than the effects of those other studied stresses on growth and yield traits.