The minimum O2 needed to fuel the demand of aquatic animals is commonly observed to increase with temperature, driven by accelerating metabolism. However, recent measurements of critical O2 thresholds ("Pcrit") reveal more complex patterns, including those with a minimum at an intermediate thermal "optimum". To discern the prevalence, physiological drivers, and biogeographic manifestations of such curves, we analyze new experimental and biogeographic data using a general dynamic model of aquatic water breathers. The model simulates the transfer of oxygen from ambient water through a boundary layer and into animal tissues driven by temperature-dependent rates of metabolism, diffusive gas exchange, and ventilatory and circulatory systems with O2-protein binding. We find that a thermal optimum in Pcrit can arise even when all physiological rates increase steadily with temperature. This occurs when O2 supply at low temperatures is limited by a process that is more temperature sensitive than metabolism, but becomes limited by a less sensitive process at warmer temperatures. Analysis of published species respiratory traits suggests that this scenario is not uncommon in marine biota, with ventilation and circulation limiting supply under cold conditions and diffusion limiting supply at high temperatures. Using occurrence data, we show that species with these physiological traits inhabit lowest O2 waters near the optimal temperature for hypoxia tolerance and are restricted to higher O2 at temperatures above and below this optimum. Our results imply that hypoxia tolerance can decline under both cold and warm conditions and thus may influence both poleward and equatorward species range limits.