“Anthropogenic global warming is redistributing marine life and may threaten tropical benthic invertebrates with several potential extinction mechanisms. The net impact of climate change on geographical extinction risk nevertheless remains uncertain. Evidence of widespread climate-driven extinctions and of potentially unidentified mechanisms exists in the fossil record. We quantify organism extinction risk across thermal habitats, estimated by paleoclimate reconstructions, over the past 300 million years. Extinction patterns at seven known events of rapid global warming (hyperthermals) differ significantly from typical patterns, resembling those driven by global geometry under simulated global warming. As isotherms move poleward with warming, the interaction between the geometry of the globe and the temperature-latitude relationship causes an uneven loss of thermal habitat and a bimodal latitudinal distribution of extinctions. Genera with thermal optima warmer than ~21°C show raised extinction odds, while extinction odds continually increase for genera with optima below ~11°C. Genera preferring intermediate temperatures generally have no additional extinction risk during hyperthermals, except under extreme conditions as the end-Permian mass extinction. Widespread present-day climate-driven range shifts indicate that occupancy loss is already underway. Given the most-likely projections of modern warming, our model, validated by seven past hyperthermal events, indicates that sustained warming has the potential to annihilate cold-water habitat and its endemic species completely within centuries.” Read in Global Change Biology