SignificanceEnergetic constraints of flight and thermoregulation have long been thought to explain why most bat species are small and live predominantly in warm latitudes. We use physical models to investigate how body size, wing shape, and climate modulate these energetic constraints. Our model predicts that thermoregulatory and flight costs, respectively, impose upper and lower bounds on the wing surface-to-mass ratio, giving rise to an optimum shape, and that variations around this optimum are more constrained in cold regions. A comparative analysis across bat species supports the model’s predictions, suggesting that body shape evolves toward an optimum with stronger selective pressures in cold regions. The model and data together suggest that thermoregulatory and locomotory constraints modulate the evolution of bats’ morphology.