Do you have a source for
> NO ANIMAL ON THIS PLANET
My guess is that cockroach will be fine. Perhaps no all species of cockroach.
Some animals have a wide distribution. Sparrows live in a wide range of climate, they have different size (in cold climates, they are bigger). Many birds migrate, some of them can probably change the extremes of the migration path and be fine.
I'm more worried for elephants and other animals with a long lifespan and small area where they can survive. (And I'm more worried about trees, because they can't move.)
Where have all the sparrows gone? https://blog.nature.org/science/2019/03/25/where-have-all-th...
Global warming is changing the rate of how fast local habitats change and therefore NO ANIMAL ON THIS PLANET is likely going to be able to handle the rate of change. Which is why we are in the 6th mass extinction.
In other words, animal life is locally calibrated, not globally and if you change the global system (therefore changing every local system quickly) you will get a bad bad situation.