Thats because you have enough thermal mass and evaporative cooling capacity to withstand those temperatures for a short period of time - ie, very little of your body will experience drastically elevated temperatures for long - if at all. Remember that air (even humid air) is not a super great heat conductor - so while the air might be very hot, it's going to be pretty bad transferring that into your body, which in turn has a lot of mass to distrube heat over, and good conductivity to move heat away from contact areas. And that whole sweat thing works pretty well too (especially in a dry sauna).

Being submerged into a 90 degree water bath will probably rapidly hideously wound you and/or kill you.

That small organisms cannot survive saunas, only large organisms with temperature regulation ("warm-blooded"), is probably a design feature.

This and because you don't stay in a Sauna for more than a few hours