Geologically rapid climate change is anticipated to increase extinction risk non-uniformly across the Earth’s surface. Tropical species may be more vulnerable than temperate species to current climate warming because of high tropical climate velocities and reduced seawater oxygen levels. To test if rapid warming indeed preferentially increased the extinction risk of tropical fossil taxa, we combine a robust statistical assessment of latitudinal extinction selectivity (LES) with the dominant views on climate change occurring at ancient extinction crises. Using a global dataset of marine fossil occurrences, we assess extinction rates for tropical and temperate genera, applying log-ratios to assess effect size and Akaike weights for model support. Among the classical ‘Big Five’ mass extinction episodes, the end-Permian mass extinction exhibits temperate preference of extinctions, whereas the Late Devonian and end-Triassic selectively hit tropical genera. Simple links between the inferred direction of climate change and LES are idiosyncratic, both during crisis and background intervals. More complex models, including sampling patterns and changes in the latitudinal distribution of continental shelf area, show tropical LES to be generally associated with raised tropical heat and temperate LES with global cold temperatures. With implications for the future, our paper demonstrates the consistency of high tropical temperatures, habitat loss and the capacity of both to interact in generating geographic patterns in extinctions.