The past relationship between global temperature and levels of biological diversity is of increasing concern due to anthropogenic climate warming. However, no consistent link between these variables has yet been demonstrated. We analysed the fossil record for the last 520 Myr against estimates of low latitude sea surface temperature for the same period. We found that global biodiversity (the richness of families and genera) is related to temperature and has been relatively low during warm 'greenhouse' phases, while during the same phases extinction and origination rates of taxonomic lineages have been relatively high. These findings are consistent for terrestrial and marine environments and are robust to a number of alternative assumptions and potential biases. Our results provide the first clear evidence that global climate may explain substantial variation in the fossil record in a simple and consistent manner. Our findings may have implications for extinction and biodiversity change under future climate warming.