As a Finn, I might have some expertise on Finnish saunas haha. I have been in a sauna for a couple of times in my belt, but it doesn't really work that well. The cleaning effect comes from sweating: more or less sweat from the glands pushes anything else on its way away, and when you rinse, you feel very clean afterwards.
Yes, only private saunas are possible. A swimsuit would be a very odd thing to wear, it would attract almost as much attention as the bare belt 😂
However, yes, the belt is against the skin, which means I will not get any warmer than your body temperature. It's perfectly safe in that sense. The reason why necklaces often become hot is that when you sit crouched in the sauna, the necklace hangs freely in the air, meaning that your body isn't there to cool it down in the same way that it would be in the case of a chastity belt.
Laura Nope. You should wear a swimsuit. At least in USA
Nope, very unhygienic. And, the residual chlorine from use in swimming pools vaporizes and causes irritation.
Speaking of which, time for our weekly family sauna!