I had to keep my quarantine tank in my bathroom temporarily. I was paranoid about temp changes as well and I would check the thermometer before and after showering, it never changed.
Make sure you use a heater that is adjustable and has a thermostat, so it will not overheat or anything. Also turn on the bathroom fan during showering so it doesnt get too stuffy.
I think it would be okay to permanently keep a tank in the bathroom given what I mentioned above.
If only I had the money, I'd have a tank in there permanently! :P