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Wrap the outside of the toilet tank in fabric. Add a tray under the toilet to catch dripping water. Replace your current tank with an insulated one. Buy a low-flow, insulated replacement toilet. Install a tempering valve to warm the water entering the tank. Invest in a tempering tank.
Purchase a premade tank cover, or use a piece of fabric to wrap around the toilet tank. Terry cloth—that is, towel material—is a commonly chosen fabric for this application. The fabric will absorb any condensation that accumulates on the outside of the tank. You'll need to wash and dry this cover every week or so to prevent mildew buildup. So, consider buying at least two covers. This method won't actually stop the tank sweat, but it will prevent it from damaging the floor under your toilet. You can buy one-size-fits-most trays for around $10 USD, or look for an under-toilet tray that is made for your particular type of toilet.  This tray will need to be emptied regularly—perhaps multiple times a day when it's particularly hot and humid. Water damage to the flooring and supporting floor structure beneath a toilet can result in very costly repairs. Do not ignore water that is dripping on the floor around your toilet. Many modern toilets have insulated tanks, which should prevent sweating. If you have an older toilet or uninsulated tank, you may be able to find a compatible insulated tank for your toilet.  Write down the brand and model of your current toilet, if you have that information, and head to a plumbing supply store. Replacing the tank alone can be more convenient, but often you'll find that replacing the entire toilet is a more feasible option. Low-flow toilets have smaller tanks, which means they have less cool water to cool down the tank walls, which results in less condensation. Also, most modern low-flow toilets have insulated tanks, which also cut back on condensation.  Especially if you have an older toilet, a newer model will significantly reduce your water consumption per flush.  Installing a toilet can be a manageable DIY project for 1-2 people, or you may prefer to hire a plumber. This valve connects to the cold water line going into the toilet as well as the hot water line. Mixing in some hot water increases the temperature of the water going into the tank, thereby reducing toilet tank condensation. The intake of hot water can also be shut off when tempering is not needed—during winter, for example. Unless your water lines are easily accessible—such as via the basement beneath the bathroom—and you have decent plumbing skills, installing a tempering valve is best left to a professional plumber. This works in a similar fashion to the tempering valve. In this case, though, the cold water line feeds into a separate holding tank, which warms the water before sending it to the toilet. This job requires open access to the water lines and enough space for the tank, among other complications. You'll almost certainly have to hire a pro to do the installation.