I think there definitely will be another round of extinctions, but the thing about extinctions is that they usually bring about another explosion/dominance of life. An example of this is the Cambrian explosion that allowed for most of life as we know to prosper or the extinction of the dinosaurs that allowed mammalians to develop/evolve. The deeper implications is that humans are going to be in control of this process of letting animals go extinct or not so maybe a hotter climate might not turn out the way we usually expect it to go.