Just like humans wanting to escape to Broome in winter here in Australia, or Florida in the USA, mammals appear to thrive in warmer temperatures according to many research papers over a few years, summarised here:
Mammals in a CO2-Enriched and Warmer World — Summary (27 April 2015)
Under such environmental circumstances (the latter of which is highly speculative) would Earth’s mammals have a difficult time surviving? … with some of them actually being driven to extinction??…
Here the extinction process happens because of land clearing and introduced feral animals and plants. Cane toads and foxes have been bad news in Australia since they were introduced.