Thermal power plants use fossil fuels or nuclear material to generate most of the world’s electricity. On hot days, when electricity demand peaks, the ambient air and water used to cool these plants can become too warm, forcing operators to curtail electricity output. Using all available observed daily-scale plant outage data, we estimate the observed dependence of thermal plant curtailment on temperature and runoff and use this relationship to quantify curtailments due to global warming. Climate change to date has increased average thermal power plant curtailment in nuclear, coal, oil, and natural gas fired plants by 0.75–1 percentage points; with each degree Celsius of additional warming, we project curtailment to increase by 0.8–1.2 percentage points during peak demand, requiring an additional 18–27 GW of capacity, or 40–60 additional average-sized power plants, to offset this global power loss. Relative to policy scenarios with global transitions to renewable portfolios or that allow aging plants to retire, thermal power generation is a systemically disadvantaged means of electricity production in a warming world. Our results point to the crucial need for additional operational data across a diversity of thermal power plants to better constrain the risks warming poses to our electricity supply.