SummaryAs the air temperature of the Earth rises, ecological relationships within a community might shift, in part due to differences in the thermal physiology of species. Prediction of these shifts -an urgent task for ecologists -will be complicated if thermal tolerance itself can rapidly evolve. Here, we employ a mechanistic approach to predict the potential for rapid evolution of thermal tolerance in the intertidal limpet Lottia gigantea. Using biophysical principles to predict body temperature as a function of the state of the environment, and an environmental bootstrap procedure to predict how the environment fluctuates through time, we create hypothetical time-series of limpet body temperatures, which are in turn used as a test platform for a mechanistic evolutionary model of thermal tolerance. Our simulations suggest that environmentally driven stochastic variation of L.ï gigantea body temperature results in rapid evolution of a substantial Ê»safety marginÊŒ: the average lethal limit is 5-7°C above the average annual maximum temperature. This predicted safety margin approximately matches that found in nature, and once established is sufficient, in our simulations, to allow some limpet populations to survive a drastic, century-long increase in air temperature. By contrast, in the absence of environmental stochasticity, the safety margin is dramatically reduced. We suggest that the risk of exceeding the safety margin, rather than the absolute value of the safety margin, plays an underappreciated role in the evolution of thermal tolerance. Our predictions are based on a simple, hypothetical, allelic model that connects genetics to thermal physiology. To move beyond this simple model -and thereby potentially to predict differential evolution among populations and among species -will require significant advances in our ability to translate the details of thermal histories into physiological and population-genetic consequences.