I've run out the front door of a house then around and back in the back door at around 10 F. . .in a bathing suit and a t-shirt. . .no harm done. . .the worst part of it was my bare feet on the cold cold ground.
Some saunas, especially traditional style ones, go up toward 190, or at least I saw references to traditional Swedish saunas at highs around 193 F.
So I don't much see the hits. . .it's certainly exhausting to do anything but sit above 130 or so, and cold saps your ability to function. . .both seem like exhaustion drains, and are applied as mods to exhaustion already.
at 0 F on the other hand, you'll stick to metal or stone, and above 200 F you're approaching the boiling point of water, so it's major damage time.