[out_of_protocol]

> How are you suffering equal heat stress from being submerged in moderately warm water

by the rules of this universe, you can't survive being submerged in 40C water for a prolonged period of time (even 37C would kill you as well), because humans produce heat and if you can't dispose of it you'll overheat and be dead soon enough

[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.