Climate and the Origin and Demise of Species
Erwin, D.H. 2009. Climate as a driver of evolutionary change. Current Biology 19: R575-R583.
Headquartered in the Department of Paleobiology at the National Museum of Natural History in Washington, DC (USA), Erwin writes that "some of the best evidence for a link between biodiversity and climate comes from latitudinal gradients in diversity, which provide an avenue to explore the more general relationship between climate and evolution." In reviewing that evidence, he indicates that "among the wide range of biotic hypotheses, those with the greatest empirical support indicate that warmer climates  have provided the energetic foundation for increased biodiversity by fostering greater population size and thus increased extinction resistance,  have increased metabolic scope,  have allowed more species to exploit specialized niches as a result of greater available energy, and  have generated faster speciation and/or lower extinction rates." And he states that "in combination with geologic evidence for carbon dioxide levels and changing areas of tropical seas, these observations provide the basis for a simple, first-order model of the relationship between climate through the Phanerozoic and evolutionary patterns and diversity," while further noting that "such a model suggests that we should expect greatest marine diversity during globally warm intervals," as is typically also found to be the case for terrestrial diversity.
Elaborating a bit, Erwin writes that "the three best-studied mass extinction events are associated with sharp changes in climate and support the contention that rapid shifts in climate can reduce global diversity," which sounds a lot like the mantra of the IPCC with respect to global warming. However, the climate shifts Erwin cites consist mostly of cooling; and it is not only the shift to cooling but stagnating in a cool state that bodes badly for earth's biodiversity. As he describes it, "the long interval of stagnant evolution during the Permo-Carboniferous glaciation is consistent with studies of modern-day latitudinal diversity that [indicate that] rates of evolutionary innovation and diversification are higher in high-energy climates than in low-energy climates."
In further explanation of this conceptual framework, Erwin notes that "contemporary studies suggest a positive relationship between high-energy climates and  increased diversification rates,  increased number of niches because of increased metabolic scope, and  more specialized niches, and possibly because of  niche construction." Indeed, he says that "studies showing that the tropics are a cradle of diversity, pumping clade representatives into higher latitudes, as well as evidence of increased ordinal level originations in the tropics, and of the sudden appearance of several mammalian groups during the Paleocene-Eocene Thermal Maximum suggest an asymmetric pattern of innovations associated with high-energy climate regimes."
Erwin's parting comment in this regard is his statement that "there is an intriguing possibility that diversity does not track climate, but rather builds up during warm intervals but without falling by proportional amounts when climates turn cooler," with the result that "warmer climates may serve as an evolutionary diversification pump with higher diversity persisting [throughout following cooler periods], at least for a time."
Whatever the case, two generalizations can clearly be made: warmth typically begets speciation, while cold tends to lead to species extinctions.