The temperature doesn’t have to be extreme to be harmful. For example, the considerable heat generated by a warm shower along with the humidity involved make a dangerous environment for a watch.
Alternatively, purchase an inexpensive watch that you wouldn’t mind getting dirty or scratched. There are also more pricey options designed for wear and tear if you’re unable to avoid high activity entirely. Bertucci A-2S is a good, scratch-resistant watch.
If unavoidable, look for “anti-magnetic” watches which include technology to prevent damage from magnets.
It’s almost always best to have your batteries replaced by a professional. For the most part, you should only change your own watch’s battery if it is both digital and not water resistant. Digital watches are without the complex mechanics which might get damaged when changing a battery. If not water resistant, there’s no seal to check after the fact. At any given moment, make sure the crown of watch is screwed or pushed in. Having it out may also affect water resistance in some watches. [3] X Research source
If you’ve got a leather band that needs cleaning, dip it in the same soapy solution, brush it and rinse with clean water. Leave out to dry, but be sure to keep the damp leather away from any source of heat.
If you’re storing watches near one another, make sure to have something to keep them from contact, to avoid scratches on the glass. For something on the cheap use acid-free tissue paper wadded up as an effective barrier. Don’t use bubble wrap as protective storing. The packaging can retain moisture, causing rust or other damage. [5] X Research source
