An anti-sweat valve that mixes a small amount of hot water with the cold water flowing into the tank can raise the tank temperature just enough to keep moisture from condensing on it. Some valves have a manual control to vary the mixture for different humidity levels.
Reasons Toilets Sweat (Condensation)
The first thing to remember is that when a cold surface contacts warmer moist air, moisture will condense on the colder surface. Such condensation causes sweating toilet tanks, and over time this moisture can rot the floor. Insulation kits are available to prevent this. They require that the tank be flushed and dry.
Second, after drying the tank thoroughly, follow the manufacturer’s instructions to cut pieces from the insulation kit. You can make this job easier by making templates from stiff cardboard and using them to outline the insulation panels.
And, finally, test-fit the insulation and apply silicone caulk or the adhesive recommended by the manufacturer to the backside of the panels. Insert the panels in the tank and apply pressure as you are fitting them. Let the adhesive cure completely. Turn the water on and adjust the float valve if necessary. These panels can displace the water just enough that a slight adjustment will do the trick for efficient flushing.