There historically hasn't been much mass extinction in hot phases. It usually seems to happen when cold, especially if an asteroid has hit the place. I guess hot, life can move towards the poles, cold if everywhere freezes and plants die life is a bit screwed.

We should ask this to an archeologist, but If I remember correctly we dodge the bullet a few times. Almost gone 900.000 years ago. Human DNA points to several genetical bottlenecks.

There is no scientific consensus that global warming will be a mass extinction event that would threaten humanity.

You're in one right now.

Literally the Ice Age, with cave-man era technology.