[lxgr]

The goal isn't to not survive though, is it?

So while I definitely think it's possible that hot baths and sauna have similar effects, I don't think this can be shown by simple thermodynamics and would require medical studies. Some sibling comments have already mentioned some.

To be clear, my objection was only to the supposed explanation/assertion of resulting core temperature being all that matters, not to the possibility that that's true.