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 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, a 16-fold improvement over prior studies, under four climate emissions scenarios. We use a novel statistical downscaling method which is significantly more skillful than the standard method, especially at near-coastal pixels where many reefs are found. 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 91% and 79% of 1 km reefs have exceeded TD10Y and TD5Y, respectively, suggesting that widespread long-term coral degradation is no longer avoidable. We project 99% of reefs to exceed TD5Y by 2034, 2036, and 2040 under SSP5-8.5, SSP3-7.0, and SSP2-4.5 respectively. We project that 2%-5% of reef locations remain below TD5Y at 1.5 degrees Celsius of mean global heating, but 0% remain at 2.0 degrees Celsius. 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.