Homeostasis.
That would be the process in which our body keeps everything *essentially* the same, from our blood, to the chemical maelstrom , to O2 levels, to our temp.
It burns more calories for our body to cool us down (hence why you'll see people running in garbage bags), than it does to warm us up (not including fevers, or hypothermic conditions in cold weather). But burn them our body does, and out temp stays essentially the same (between 97 & 99). Yay for warmbloodedness.
Your baby not only has your own body maintaining homeostasis, but it's got several walls of insulation, plus that whole swimming pool of amniotic fluid. They quite literally have a thermos within a thermos.
The point of this? Hot baths are FINE. Great even, for relaxing sore muscles. Even hottubs are fine BUT with hottubs you have to be careful, because they don't cool down as you're in them like baths do. But you can still hottub...you just have to get out a lot sooner than you otherwise would (you'll WANT to, to...if you start feeling dizzy...you should have gotten out 5 min before...because your body has to work extra hard to maintain homeostasis. But maintain it it will, to a point. That dizziness is the point wherein your body has started to LOSE it's grip on homeostasis.)
So you've got homeostasis, and that amazing babygrowing chamber that protects it from the world on your side. You've also got this:
Women have been carrying healthy, happy babies to term in deserts and jungles around the world for millennium, and still do. Where the temp is over 100 degrees every day. In some times/places over 115. Temp your bath next time you take one. Is it over 115? probably to start out with, but 115 is the temp bath water usually hangs out in for the majority of the time. About 110 and most of us get out. (110 is also the perfect temp for kids hot chocolate) And do you stay in 115 degree water for 12 hours? No? You should be fine.
Just listen to your body. If it feels good, have at...if you feel lousy/sweaty/dizzy or otherwise bad, it's telling you you're working to hard. You may also try taking a glass of ice water in with you, to stay hydrated (hydration = easier to maintain homeostasis)
So take those warm baths. It's not like your wee one is going to get soap in their eyes, it's a sealed system, after all. :)