Whether species are capable of adapting to rapid shifts in climate raises considerable interest. Analyses based on niche models often assume niche conservatism and equilibrium with climate, implying that species will persist only in regions where future climatic conditions match their current conditions and that they will colonize these regions promptly. However, species may adapt to changing climate and persist where future climates differ from their current optimum. Here, we provide a first macroecological generalization to the approach of evolutionary rescue, by comparing the expected shift in mean temperature within the geographic range of 7193 species of amphibians worldwide, under alternative warming scenarios. Expected evolutionary change is expressed in units of standard deviations of mean temperature, per generation (Haldanes) and compared with theoretical models defining the maximum sustainable evolutionary rates (MSER) for each species. For the pessimistic emission scenario RCP8.5, shifts in mean temperature vary between near-zero and 6°C within the geographic ranges for most species, with a median equal to 3.75°C. The probability of evolutionary rescue in temperature peaks is higher than 0.05 for about 55% of the species and higher than 0.95 for only 12% of the species. Therefore, the predicted shift in mean temperature would be too extreme to deal with for almost half of the species. When evolutionary plasticity is incorporated, this scenario becomes more optimistic, with about 44% of the species being likely to shift their thermal peaks tracking future warming. These figures are not random in geographical space: evolutionary rescue would be unlikely in the tropics, especially in South America (Amazonia), parts of Africa, Indonesia, and in the Mediterranean region. Given the uncertainty in demographic and genetic parameters for species’ responses to climate change, we caution that it remains difficult to assess the realism of the macroecological generalization. In any case, it may be precautionary to assume that our results are not liberal, showing low probability of adaptation for most of the species and thus that the persistence of populations by evolutionary rescue may, in general, be unlikely in the long term.