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ABSTRACT Comparative phylogenetic studies of adaptation are uncommon in biomechanics and physiology. Such studies require data collection from many species, a challenge when this is experimentally intensive. Moreover, researchers struggle to employ the most biologically appropriate phylogenetic tools for identifying adaptive evolution. Here, we detail an established but greatly underutilized phylogenetic comparative framework – the Ornstein–Uhlenbeck process – that explicitly models long-term adaptation. We discuss challenges in implementing and interpreting the model, and we outline potential solutions. We demonstrate use of the model through studying the evolution of thermal physiology in treefrogs. Frogs of the family Hylidae have twice colonized the temperate zone from the tropics, and such colonization likely involved a fundamental change in physiology due to colder and more seasonal temperatures. However, which traits changed to allow colonization is unclear. We measured cold tolerance and characterized thermal performance curves in jumping for 12 species of treefrogs distributed from the Neotropics to temperate North America. We then conducted phylogenetic comparative analyses to examine how tolerances and performance curves evolved and to test whether that evolution was adaptive. We found that tolerance to low temperatures increased with the transition to the temperate zone. In contrast, jumping well at colder temperatures was unrelated to biogeography and thus did not adapt during dispersal. Overall, our study shows how comparative phylogenetic methods can be leveraged in biomechanics and physiology to test the evolutionary drivers of variation among species.