The climatic variability hypothesis posits that the magnitude of climatic variability increases with latitude, elevation, or both, and that greater variability selects for organisms with broader temperature tolerances, enabling them to be geographically widespread. We tested this classical hypothesis for the elevational range sizes of more than 16,500 terrestrial vertebrates on 180 montane gradients. In support of the hypothesis, mean elevational range size was positively correlated with the scope of seasonal temperature variation, whereas elevational range size was negatively correlated with daily temperature variation among gradients. In accordance with a previous life history model and our extended versions of it, our findings indicate that physiological specialization may be favored under shorter-term climatic variability.