Actually, it is. For most mammals a temperature over around 31C at 100% humidity is lethal after no more than six hours of exposure.

Go beyond that and everyone dies.

I haven't seen any projected warming scenario where it'd be 31C everywhere. There's a gradual change in habitability as the habitable zone becomes smaller and smaller.

Perhaps our descendants will be farming Antarctica.

Sure, but will humans just sit idle by and wait for extinction, or will they do whatever it is necessary to keep the ecosystem from boiling away? Of course it depends on how severe the problem is, but in general we have the means to affect climate. (Solar shade comes to mind and large scale GHG capture.)

You're right to a point. The hotter it gets on average, the faster the less fit die due to various heat related reasons. Once it hits 31c@100% relative humidity, land mammals die.

So it's on a rolling scale up to 31C. At or past, yeah its a binary cliff.