I'd guess that most people have a similar problem given the current weather.
There is one way to reduce it and another to stop it ...
If you have a flush/syphon valve with an adjustable flush tab on the side.
Reduce the amount of water being used for a flush. This way less icy cold water enters the cistern and reduces the amount of condensation created.
It does work, about six weeks ago I replaced our dual flush valve and fitted an adjustable one, the condensation has just about gone.
Yesterday I removed it and increased the flush volume ... the condensation has returned ... as most of the dual flush mechanisms have bayonet type fitting, it only takes seconds to remove and adjust it.
If you want to eliminate the condensation ... connect your cistern to your hot water supply ... I know two people who have done it, and they dont have the problem anymore ... it's not very green though, as your boiler fires up every time the toilet is flushed.
furthermore, connecting to the hot water supply simply wouldn't work. most modern cisterns only take about 6 litres of water, all you will be doing is replenishing the water with the cold standing water in the pipes - the hot water probably won't even make it to the cistern.
and if running a combi the same applies - by the time the combi has heated the water the cistern will already be recharged, the float valve will have shut off the incoming water and the boiler will have fired up for nothing. you would potentially run the risk of overheating and damaging the boiler if done on a regular basis which is likely, given how often a toilet is flushed.
Condensation on a toilet tank is caused by the water in the tank cooling the surface of the tank. This causes water vapor in the air to turn back to liquid water upon contact with the cool ceramic surface.
There are a few different ways to deal with this problem. The first is to increase the water temperature in the cold line. This can be done by installing a mixing valve between the hot water heater and the cold water line to the toilet. The valve will add a little hot water to bring the temperature up. I don't suggest doing this for your entire home water system, since hot water carries more mineral contaminants and is usually not recommended for drinking water.
connecting your hot water supply to your toilet cistern is a crazy idea. i've never heard of such gadgets and certainly would not use one if i did manage to find one.
it's a waste of money and would not work! there is a purpose made product on the market that will cure this problem, a simple liner that goes inside the cistern and insulates the ceramic from the cold water. very cheap, quick and easy to fix.
why then go to all the trouble of over engineering a solution that will never work?