Thermal refugia underpin climate-smart management of coral reefs, but whether current thermal refugia will remain so under future warming is uncertain. We use statistical downscaling to provide the highest resolution thermal stress projections (0.01°/1 km, >230,000 reef pixels) currently available for coral reefs and identify future refugia on locally manageable scales. Here, we show that climate change will overwhelm current local-scale refugia, with declines in global thermal refugia from 84% of global coral reef pixels in the present-day climate to 0.2% at 1.5°C, and 0% at 2.0°C of global warming. Local-scale oceanographic features such as upwelling and strong ocean currents only rarely provide future thermal refugia. We confirm that warming of 1.5°C relative to pre-industrial levels will be catastrophic for coral reefs. Focusing management efforts on thermal refugia may only be effective in the short-term. Promoting adaptation to higher temperatures and facilitating migration will instead be needed to secure coral reef survival.