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Understanding rates and patterns of change in physiological and climatic-niche variables is of urgent importance as many species are increasingly threatened by rising global temperatures. Here, we broadly test several fundamental hypotheses about physiological and niche evolution for the first time (with appropriate phylogenetic methods), using published data from 2059 vertebrate species. Our main results show that: (i) physiological tolerances to heat evolve more slowly than those to cold, (ii) the hottest climatic-niche temperatures change more slowly than the coldest climatic-niche temperatures, and (iii) physiological tolerances to heat and cold evolve more slowly than the corresponding climatic-niche variables. Physiological tolerances are significantly and positively related to the corresponding climatic-niche variables, but species often occur in climates outside the range of these tolerances. However, mismatches between climate and physiology do not necessarily mean that the climatic-niche data are misleading. Instead, some standard physiological variables used in vertebrates (i.e. critical thermal maxima and minima) may reflect when species are active (daily, seasonally) and their local-scale microhabitats (sun versus shade), rather than their large-scale climatic distributions.