Bats are a unique mammalian group, which belong to one of the largest and most diverse mammalian radiations, but their early diversification is still poorly understood, and conflicting hypotheses have emerged regarding their biogeographic history. Understanding their diversification is crucial for untangling the enigmatic evolutionary history of bats. In this study, we elucidated the rate of diversification and the biogeographic history of extant bat lineages using genus-level chronograms. The results suggest that a rapid adaptive radiation persisted from the emergence of crown bats until the Early Eocene Climatic Optimum, whereas there was a major deceleration in diversification around 35–49 Ma. There was a positive association between changes in the palaeotemperature and the net diversification rate until 35 Ma, which suggests that the palaeotemperature may have played an important role in the regulation of ecological opportunities. By contrast, there were unexpectedly higher diversification rates around 25–35 Ma during a period characterized by intense and long-lasting global cooling, which implies that intrinsic innovations or adaptations may have released some lineages from the intense selective pressures associated with these severe conditions. Our reconstruction of the ancestral distribution suggests an Asian origin for bats, thereby indicating that the current panglobal but disjunct distribution pattern of extant bats may be related to events involving seriate cross-continental dispersal and local extinction, as well as the influence of geological events and the expansion and contraction of megathermal rainforests during the Tertiary.