The condensation is due to the humidity and temperature differential. to prevent it you will need to remove one of the causative factors. The fresh new cold water that enters the tank....or the humid air in the bath room from "contacting" the tank. Most install vents to suck out the humid air, some put "covers" on the toilet tank to insulate the cold water from the humid air...I have yet to see one plumbed with hot ( or tempered) water.
Given enough time the tank will equilibrate with the room temp and the condensation will not form.
Is this an new installation or how old is the toilet? How long has the condensation been forming? Humidity is the cause....is there an exhaust fan in the bath? If not...add one...if so...put it on a timer switch to run for about 20minutes after each shower. Make sure the exhaust is properly ducted to the outside. Removing moisture from the bath after showers should help.
Is there hvac service to the bath? If so, check to make sure the duct is open. Air circulation will also help rid you of the problem. Do you have a humidifier on your hvac system? Is the condensation forming all the time or only during the heating season? If you have a humidifier on your hvac system it maybe raising the levels to high in the bath and can be adjusted.
They do make a foam tank liner to help insulate the inside of the toilet tank. You'll need to check with your local hardware store to see what they have. I've heard of them but HandyANDY has never had a cause to use one.
Let us know how it goes
Those power flush units would solve the problem too...this is the type of toilet that has a plastic "pressure tank" inside the normal ceramic tank. Here an air break would be there...though the condensate may still form on the sides of the plastic tank inside the regular tank.
Try using a dehumidifier. My friend bought a new house a few years back, and the construction plumbers connected the hot water to the toilets. No condensation, just steam. I don't recommend that. You may have very cold water coming into the bathroom from water piped in the basement? My pipes are in the attic, so the water is heated up and condensation is not an issue. We also in So. Cal. have very low humidity.
I store my shower rugs on top of my toilet, between the lid and the shelf thingy above. That way I can trade out the rug as needed, and I never actually have seen condensation since i started doing this. I guess it was not an issue for me, but I do remember seeing it prior to storing those little oval thick cotton floor rugs. I fold them in thirds to fit, and about 5 can be squeezed in between that and the over-the-toilet shelf thing.