This study sought to identify climate-change thermal-stress refugia for reef corals in the Indian and Pacific Oceans. A species distribution modeling approach was used to identify refugia for 12 coral species that differed considerably in their local response to thermal stress. We hypothesized that the local response of coral species to thermal stress might be similarly reflected as a regional response to climate change. We assessed the contemporary geographic range of each species and determined their temperature and irradiance preferences using a k-fold algorithm to randomly select training and evaluation sites. That information was applied to downscaled outputs of global climate models to predict where each species is likely to exist by the year 2100. Our model was run with and without a 1°C capacity to adapt to the rising ocean temperature. The results show a positive exponential relationship between the current area of habitat that coral species occupy and the predicted area of habitat that they will occupy by 2100. There was considerable decoupling between scales of response, however, and with further ocean warming some 'winners' at local scales will likely become 'losers' at regional scales. We predicted that nine of the 12 species examined will lose 24-50% of their current habitat. Most reductions are predicted to occur between the latitudes 5-15°, in both hemispheres. Yet when we modeled a 1°C capacity to adapt, two ubiquitous species, Acropora hyacinthus and Acropora digitifera, were predicted to retain much of their current habitat. By contrast, the thermally tolerant Porites lobata is expected to increase its current distribution by 14%, particularly southward along the east and west coasts of Australia. Five areas were identified as Indian Ocean refugia, and seven areas were identified as Pacific Ocean refugia for reef corals under climate change. All 12 of these reef-coral refugia deserve high-conservation status.