For embryos that develop within eggs, a fundamental problem posed by warming is that their demand for oxygen increases much more rapidly with temperature than their capacity for supply, which is constrained by diffusion across the egg surface. Thus, as temperatures rise eggs may experience oxygen limitation due to an imbalance between oxygen supply and demand. Here we formulate a mathematical model of oxygen limitation and experimentally test whether this mechanism underlies the upper thermal tolerance in large aquatic eggs. Using Chinook salmon (Oncorhynchus tshawytscha) as a model system, we show that the thermal tolerance of eggs is not fixed but instead varies systematically with features of the organism and environment. Importantly, this variation can be precisely predicted by the degree to which these features shift the balance between oxygen supply and demand. Equipped with this mechanistic understanding we predict and experimentally confirm that the thermal tolerance of these embryos in their natural habitat is substantially lower than expected from laboratory experiments performed under normoxia. More generally, we show how complex patterns of context-dependent thermal tolerance can be predicted from simple biophysical theory.