Analyses of evolutionary radiations have traditionally focused on traits related to resource acquisition, habitat use, and mate choice. Nonetheless, incorporation of climatic niche divergence has become more common in recent years, driven by the development of correlative ecological niche models (ENMs) that allow niche characterization based solely on geo-referenced locality data. However, ENMs require no data on organismal traits that link climatic conditions to performance, and thus have little to say about how organisms phenotypically adapt to different climatic conditions, what the performance consequences of phenotypic divergence are, and how phenotypic divergence influences resource partitioning within communities of co-occurring species. Here, we conduct a functional (i.e., physiological) analysis of climatic niche divergence within Greater Antillean Anolis radiations. We find that physiological divergence occurred repeatedly within these radiations, that there are performance consequences of physiological divergence within natural habitats, and that physiological divergence facilitates species co-existence within species-rich communities. We also use phylogenetic methods to compare rates of evolution of ecologically relevant physiological and morphological traits, and find that physiology has evolved either more slowly or as fast (but not faster) than morphology. Our analysis demonstrates the benefit of a functional approach to understanding macroevolutionary patterns of climatic niche divergence.