Model predictions of extinction risks from anthropogenic climate change are dire, but still overly simplistic. To reliably predict at-risk species we need to know which species are currently responding, which are not, and what traits are mediating the responses. For mammals, we have yet to identify overarching physiological, behavioral, or biogeographic traits determining species' responses to climate change, but they must exist. To date, 73 mammal species in North America and eight additional species worldwide have been assessed for responses to climate change, including local extirpations, range contractions and shifts, decreased abundance, phenological shifts, morphological or genetic changes. Only 52% of those species have responded as expected, 7% responded opposite to expectations, and the remaining 41% have not responded. Which mammals are and are not responding to climate change is mediated predominantly by body size and activity times (phylogenetic multivariate logistic regressions, P < 0.0001). Large mammals respond more, for example, an elk is 27 times more likely to respond to climate change than a shrew. Obligate diurnal and nocturnal mammals are more than twice as likely to respond as mammals with flexible activity times (P < 0.0001). Among the other traits examined, species with higher latitudinal and elevational ranges were more likely to respond to climate change in some analyses, whereas hibernation, heterothermy, burrowing, nesting, and study location did not influence responses. These results indicate that some mammal species can behaviorally escape climate change whereas others cannot, analogous to paleontology's climate sheltering hypothesis. Including body size and activity flexibility traits into future extinction risk forecasts should substantially improve their predictive utility for conservation and management.