We used quantitative genetics to test a controversial theory of heat stress, in which animals overheat when the demand for oxygen exceeds the supply. This theory, referred to as oxygen- and capacity-limited thermal tolerance, predicts a positive genetic correlation between hypoxia tolerance and heat tolerance. We demonstrate the first genetic correlation of this kind in a model organism, Drosophila melanogaster. Genotypes more likely to fly under hypoxic stress (12% O2) were also more likely to fly under heat stress (39°C). This finding prompts new questions about mechanisms and limits of adaptation to heat stress.