If tank condensation is in a particular situation caused by steam from the shower condensing on the tank, because of the cold water in it. how about redirecting some of the shower drain (hot) water thru the tank. You can use a heat exchanger coil of 3/4 inch copper , a small radiator,or even a direct line of 1/4 inch plastic icemaker line, of course the overflow will go down the standpipe but it will keep the tank nice and warm and cozy.
Steve,
It seems like with a properly working tank this would only be a problem in certain climates in winter. The supply water temp would have to be rather cold for condensation to occur--I've not seen this even in the subtropical southwest Georgia region. Modern toilets use small flush volumes and usually retain considerable residual water in the tank at the end of the flush (to produce a higher head stack for the flush.) This greatly reduces the temperature drop of the external tank wall compared to the older pre-1994 high volume toilets. Therefore, the tank wall is not likely to be considerably cooler than the ambient of the room. Now if someone takes high flow half hour showers with rather hot water...the tank, bowl, water line, etc. could stillsweat considerably.
Terry's point about flapper leak (or possibly porosity or hidden crack or a leaky fill valve) resulting in lower than normal tank temperatures is also a possibility worth checking.
But getting to the proposal at hand, it has big problems.
1. You have to collect the drain water--likely a vessel...one that will get dirty with hair and soap scum.
2. You have to pump (lift) the water to an elevation which it can flow through the tank.
3. There will be a lag before the tank warms. This might not matter with 50% or more of the drainwater going through the tank heat transfer tubing, but I suspect you were thinking of a lower fraction.