I'm a bather too.... For me normally when I'm not pregnant I put the water as hot as it can go so the flinch test doesn't work for me so I have just been having Luke warmish baths....
I was told by my doctor that your body will naturally think too hot of water is too hot. Temps that you probably didnt mind before are going to seem way hotter. As long as your not doing it too hot you should be fine. Ive taken baths with both my pregnancies and everyone was ok.
hot tubs are bad for you for the same reason as hot baths. it can raise your body temperature too much, which will also raise the babys body temp. you can take warm water baths.
As long as it's not too hot, there's nothing wrong with baths. I lived in one for almost 2 months straight. (Lol. It helped a lot with my nausea) Just make it warm enough to were you don't have to flinch to get in, and you can comfortably.