Despite the global ecological importance of climate change, controversy surrounds how oxygen affects the fate of aquatic ectotherms under warming. Disagreements extend to the nature of oxygen bioavailability and whether oxygen usually limits growth under warming, explaining smaller adult size. These controversies affect two influential hypotheses: gill oxygen limitation and oxygen- and capacity-limited thermal tolerance. Here, we promote deeper integration of physiological and evolutionary mechanisms. We first clarify the nature of oxygen bioavailability in water, developing a new mass-transfer model that can be adapted to compare warming impacts on organisms with different respiratory systems and flow regimes. By distinguishing aerobic energy costs of moving oxygen from environment to tissues from costs of all other functions, we predict a decline in energy-dependent fitness during hypoxia despite approximately constant total metabolic rate before reaching critically low environmental oxygen. A new measure of oxygen bioavailability that keeps costs of generating water convection constant predicts a higher thermal sensitivity of oxygen uptake in an amphipod model than do previous oxygen supply indices. More importantly, by incorporating size- and temperature-dependent costs of generating water flow, we propose that oxygen limitation at different body sizes and temperatures can be modeled mechanistically. We then report little evidence for oxygen limitation of growth and adult size under benign warming. Yet occasional oxygen limitation, we argue, may, along with other selective pressures, help maintain adaptive plastic responses to warming. Finally, we discuss how to overcome flaws in a commonly used growth model that undermine predictions of warming impacts.