Coral reefs are rapidly declining due to local environmental degradation and global climate change. In particular, corals are vulnerable to ocean heating. Anomalously hot sea surface temperatures (SSTs) create conditions for severe bleaching, the expulsion of photosynthetic algal symbionts leaving corals at risk of starvation and disease, or direct thermal death. We use SST observations and CMIP6 model SST to project thermal conditions at reef locations at a resolution of 1 km squared, a 16-fold improvement over prior studies, under future emissions scenarios. For each location we present projections of thermal departure (TD, the date after which a location with steadily increasing heat exceeds a given thermal metric) for severe bleaching recurs every 5 years (TD5Y) and every 10 years (TD10Y), accounting for a range of post-bleaching reef recovery/degradation. As of 2021, we find that over 93% and 85% of 1 km reef locations have exceeded TD10Y and TD5Y, respectively, suggesting that widespread long-term coral degradation may no longer be avoidable. We project 99% of reef locations to exceed TD5Y by 2033, 2035, and 2041 under SSP5-8.5, SSP3-7.0, and SSP2-4.5 respectively, but this milestone would not be crossed under SSP1-2.6. We project that 2% of reef locations remain below TD5Y at 1.5°C of mean global heating, but 0% remain at 2.0°C. These results demonstrate the importance of further improving ecological projection capacity for climate-vulnerable marine and terrestrial species and ecosystems, including identifying refugia and guiding conservation efforts. Ultimately, saving coral reefs will require rapidly reducing and eliminating greenhouse gas emissions.