Climate warming threatens to increase mass coral bleaching events, and several studies have projected the demise of tropical coral reefs this century. However, recent evidence indicates corals may be able to respond to thermal stress though adaptive processes (e.g., genetic adaptation, acclimatization, and symbiont shuffling). How these mechanisms might influence warming-induced bleaching remains largely unknown. This study compared how different adaptive processes could affect coral bleaching projections. We used the latest bias-corrected global sea surface temperature (SST) output from the NOAA/GFDL Earth System Model 2 (ESM2M) for the preindustrial period through 2100 to project coral bleaching trajectories. Initial results showed that, in the absence of adaptive processes, application of a preindustrial climatology to the NOAA Coral Reef Watch bleaching prediction method overpredicts the present-day bleaching frequency. This suggests that corals may have already responded adaptively to some warming over the industrial period. We then modified the prediction method so that the bleaching threshold either permanently increased in response to thermal history (e.g., simulating directional genetic selection) or temporarily increased for 2–10 years in response to a bleaching event (e.g., simulating symbiont shuffling). A bleaching threshold that changes relative to the preceding 60 years of thermal history reduced the frequency of mass bleaching events by 20–80% compared with the ‘no adaptive response’ prediction model by 2100, depending on the emissions scenario. When both types of adaptive responses were applied, up to 14% more reef cells avoided high-frequency bleaching by 2100. However, temporary increases in bleaching thresholds alone only delayed the occurrence of high-frequency bleaching by ca. 10 years in all but the lowest emissions scenario. Future research should test the rate and limit of different adaptive responses for coral species across latitudes and ocean basins to determine if and how much corals can respond to increasing thermal stress.