Have you tried walking outside in 37.8 C weather? It's blistering hot. Your body should be quite a bit warmer than the environment because we have to radiate heat away to preserve homeostasis. 21 C is a comfortable room temperature.

Well, I walk for hours, people don't sit in a tub for that long when they are washing themselves off.

The issue is that wet bulb temperatures above 35°C aren't hospitable to human life for very long. That's why sauna sessions are limited and frequently punctuated by going into the cold.

Humans radiate a lot of heat, and if we can't dump that waste heat into our environments or take advantage of evaporative cooling, we overheat. Saunas condition people to survive this for longer periods, but they're not something you could make use of in the tropics without any air conditioning, for instance.

Saunas are meant to be dry.

Banyas on the other hand... (okay, they can be both)

I find 100F to be pretty warm for the hot tub, after 15 minutes I'm too warm and ready to get out (or sit up on the top step to cool off).

We usually keep it at 101F in the winter (since it feels nice to walk out in the cold and soak for 15 minutes) and 98 in the summer -- at 97 I can stay in indefinitely, but my wife gets cold at 15 minutes, so 98 is a compromise.

I wonder if a 100 degree hot tub has a similar benefit as a hot sauna.

I'm similar— slightly warmer in the winter so you get that nice core-temp boost to enjoy afterward, plus a pillow of steam to sit in during.

But yeah, it's striking how putting it down to 96F can quite quickly make you feel a chill. And not the refreshing chill of jumping into a much-colder-than-that swimming pool, but like the bone chill of having had the heat bled out of you.

Water's specific heat capacity is such that you feel the temperature right away. I've been in 39 degree hot springs and it's almost too hot.

I have my hottub at 40C which is hot when you get in but comfortable to sit in for a while.

Me too I keep mine at 104 F