Since Charles Darwin termed it his "abominable mystery", rapid speciation in angiosperms has eluded simple explanation. Climate has been implicated as a major catalyst of diversification, but its effects are thought to be inconsistent over time, between clades and across regions of the globe. Here we test the influence of climate change and geography-related climate factors on the diversification of the orchidoid orchids, a diverse subfamily of enduring fascination since Darwin's time. We show that global cooling spurred speciation in assemblages of orchidoids throughout the earth. Employing a phylogenetic framework, we demonstrate that speciation rate is correlated with historic changes in global temperature, but not atmospheric CO2 or sea-level. Cooling-driven diversification is consistent in all tribes, and in Disa, a large genus with well-supported signatures of adaptive evolution. We find no evidence for influences of geography-related climate factors, such as latitudinal and elevation gradients, or for cradles of diversity, in analyses of tip rates in the context of 1.5 million georeferenced records. Rather than being an abominable mystery, our results support a simple hypothesis that climate change can rapidly accelerate adaptive radiation in assemblages throughout the globe. Our findings raise the possibility that there are undiagnosed roles for climate change in other major radiations and indicate how contemporary climate change will influence long-term evolutionary processes.