Quick answer: some.
Longer answer: Quintero and Wiens 2013 looked at a sample of clades across Tetrapoda (vertebrates with four limbs with phalanges IOW 'reptiles', 'amphibians', birds, and mammals) and their known climatic data (IOW, the climatic conditions of where they live). These two researchers looked at how long it took for sister species within these clades to speciate, as a proxy for seeing how long it takes for a population to adapt from one climatic regime to another, e.g., how long it takes a species to adapt into a rainforest niche if its ancestral population were savannah dwellers.
This length of time is something along the lines of 10,000 times longer than modern global warming is predicted to change Earth's climate.
For annual mean temperature (Fig. 1), the mean species rate in most of the 17 clades is less than 1°C/Myr ... In contrast, the IPCC estimated rates are ~ 4°C for mean annual temperature in the next ~ 100 years, depending on location. We find that the rate of change observed among species is typically ~ 10 000 – 100 000 times slower than the expected rate of change from 2000 to 2100 (Table 2).
The authors respectfully state that their research may have many sources of error, and that it may be presumptious to extrapolate that these findings (within some clades of Tetrapoda) are going to be equally applicable to all members of Tetrapoda, let alone all forms of animal (or non-animal) life. But modern efforts to help threatened or endangered species by preserving their current habitat may simply not cut it as the best strategy; our preserves and corridors for threatened species may have to adapt, lest we pigeonhole them into extinction.