Baths / saunas, swimming in public places, gyms, etc., as mentioned above, affect the tattoo unambiguously. The pigment loses its color, the pattern can "float". Also, a tattoo is an open wound. It's better not to joke with such matters :)
As far as I know, while the tattoo is healing, you cannot expose it to any external influences. Especially temperature. During healing, even going to the gym is not recommended, because sweating may not have a very beneficial effect on the skin that has not yet healed.
A tattoo is a wound. The wound requires protection, as any infection can be contracted, especially in such favorable conditions for bacterial growth. And also (here I am no longer an expert), I assume that the effect of temperatures on the paint will be negatively reflected, the drawing will deteriorate.