Climate change is a critical factor affecting biodiversity. However, the quantitative relationship between temperature change and extinction is unclear. Here, we analyze magnitudes and rates of temperature change and extinction rates of marine fossils through the past 450 million years (Myr). The results show that both the rate and magnitude of temperature change are significantly positively correlated with the extinction rate of marine animals. Major mass extinctions in the Phanerozoic can be linked to thresholds in climate change (warming or cooling) that equate to magnitudes >5.2 °C and rates >10 °C/Myr. The significant relationship between temperature change and extinction still exists when we exclude the five largest mass extinctions of the Phanerozoic. Our findings predict that a temperature increase of 5.2 °C above the pre-industrial level at present rates of increase would likely result in mass extinction comparable to that of the major Phanerozoic events, even without other, non-climatic anthropogenic impacts.