The heat on your boobs can induce labor also. Or simptoms of labor. (Herd it from my doc.)
My midwife said its a old wives tale only hot tubs are bad because the temp stays the same and never cools but a bath as soon as the waters off it starts to cool because nothing is keeping it at the same hot temp it just keeps cooling
A warm bath is fine but you don't want to raise your body temperature.
It's only if the water is so hot that it turns your skin red. It can increase your baby's body temperature.