It takes about 300 watt hours of energy to raise the body temperature of a human by 6 degrees. If your human is starting at 99 degrees, 6 degrees will put you at 105, which is where you'll start to have immediate problems. (At 104 you aren't going to be happy, but you are going to survive and you're not likely to sustain organ damage).

If we assume that you are putting out 100 watts, you've got 3 hours at a wet bulb of 100F before you start having risk of death (if you are well adjusted to the heat).

And yes, I spend time every month in Saunas and Hammams with extreme temperatures. My favorite room is 195 degrees and 45% humidity. That translates to something like 150 degree wet bulb temperature, and I can happily stay in that room for about 20 minutes. (though 60 minutes would probably kill me). I've also spent plenty of time in Hammams (30+ minute sessions) where the temperature was 110F and the humidity was 100% (which means the entire room is fog and it's constantly dripping everywhere, practically raining). These aren't elite extremes in the sauna world, you'll find saunas close to these conditions all over the world.