Reef-building corals thriving in extreme thermal environments may provide genetic variation that can assist the evolution of populations to rapid climate warming. However, the feasibility and scale of genetic improvements remain untested despite ongoing population declines from recurrent thermal stress events. Here, we show that corals from the hottest reefs in the world transfer sufficient heat tolerance to a naïve population sufficient to withstand end-of-century warming projections. Heat survival increased up to 84% when naïve mothers were selectively bred with fathers from the hottest reefs because of strong heritable genetic effects. We identified genomic loci associated with tolerance variation that were enriched for heat shock proteins, oxidative stress, and immune functions. Unexpectedly, several coral families exhibited survival rates and genomic associations deviating from origin predictions, including a few naïve purebreds with exceptionally high heat tolerance. Our findings highlight previously uncharacterized enhanced and intrinsic potential of coral populations to adapt to climate warming.