Most often, the toilet does its sweating during the summer months, when the humidity level is high. At this time, a lot of water vapor is in the air. When the water vapor comes in contact with the cold surface of the tank, it releases its water vapor. The vapor forms droplets that cling to the cold surface. Eventually these droplets are pulled to the floor by gravity.
Toilets that have seasonal problems with condensation sometimes can be controlled by simply running the air conditioner or placing a dehumidifier in the room. If condensation occurs all year long, a more effective exhaust fan or tighter insulation may be warranted. Small amounts of condensation can just as easily be controlled by placing a towel on the floor to catch the drips or covering the toilet tank with a fabric cover.
Tempering valves are often the best solution for toilets with severe sweating problems. They are especially useful where the water is very cold, such as in homes using well water. The tempering valve attaches to both the cold and hot water supply, providing warmer water to the toilet tank. The biggest drawback to this method is that you are flushing expensive hot water down the drain. Depending on the layout of your plumbing, it may also be difficult to isolate the line to the toilet so that other cold water supplies are not affected.
Styrofoam toilet tank liners are available at home improvement stores. The foam acts as a thermal barrier between your toilet tank and the water, reducing or eliminating external condensation. Take care that all moving parts can still maneuver freely and that all joints are tight when installing a toilet tank liner. Another low-tech option is to place an aquarium heater in the toilet tank. This works the same way as the tempering valve, although you don't have to perform a permanent installation.