If you have condensation on your toilet tank, you could be damaging your tiles or causing rot in your subfloor.
This “sweating” occurs when moist air hits the cold sides of your toilet tank, so it stands to reason that warming up the sides of the tank will cure the problem.
Of course, you could tap into a hot water supply line, and combine hot and cold to supply warmer water to the tank — if you don’t care about your heating bills. But an insulated tank is your best bet if the water coming in is not ice-cold. You can either buy an insulated replacement tank, or make your own.
Buy a kit or enough 1/2″ Styrofoam or foam rubber to cover the inside walls of the tank. Remove the cover, and put it in a safe place where it won’t be broken. Drain the tank by shutting off the supply valve, and flushing the toilet. Then bail and blot any remaining water, and make sure the sides of the tank are completely dry. Use epoxy resin cement to attach the insulating foam to the inside walls of the tank, making sure you don’t get in the way of moving parts. Make sure the insulation rises above the water line by a couple inches.
And don’t refill the tank until the epoxy is completely dry.
Insulating your tank has the added benefit of reducing the noise of the tank re-filling, and cutting down slightly on your water use.