Hugh, and posters, let's see what happens with condensation on a more basic level for clues on how to solve this.
On a hot, humid Saturday, you are at the computer when you get thirsty. You go to the refrigerator and fix a big glass of Dr. Pepper with ice in it and set that on your wood computer desk. You find an interesting site about the life cycle of the Mediteranian fruit fly or something and forget the cold glass. Then after all the excitement when you find that fruit flies are the most interesting bugs in the world, you go take a nap leaving the cold glass still sitting out.
When you wake up, you come back to the computer to find a really big puddle of water around the glass. You got a white ring on your desk top from the water sitting there so long and it serves you right! Since I don't want to have to spell out again how to fix a white ring, I'll tell you how to fix the problem.
Any cold object on a hot, humid day will have this problem and one answer is to make the object less cold. You can put one of those cutsy terry cloth tank covers on the tank. That will help a little since it insulates and gives more surface for the water to evaporate from. And you only thought that the tank cover was there because your wife did not to be reminded about bodily functions. She's the one that changed the baby, if you remember.
You may be able to glue insulation inside your tank. People have done this with more or less success using cheap, closed cell stryofoam in the big, old 3.5 GPF toilets. With the new smaller toilet tanks this is not practical. They are using the minimum amount of water to do the work as it is and you can't afford to lose any more. You can call a plumber to put in a recirculation pump. This is expensive both in first cost and running the motor. But when you turn on that shower on a cold morning and have instant hot water, it sure is nice. Say, we may be on to something here. If while the plumber was there, he put in a mixing valve in the line to the tank and a tankless water heater near the bathroom, you would really have something. Brian (Tankless) Wood would be more than happy to expand on this, I'm sure. And he can tell you how much money you can save with the tankless water heater.
No, I don't have a tankless water heater. I just put a large coaster under the tank since we have young adults that have not learned to handle their beer. LOL Or to put a coaster under the fast food drink cups either. I do have battleship linoleum on my computer desk top, as did the old office desk that it was when it was made. And I have a tile topped table next to my recliner.
The beauty of age is that by the time they have houses and mortgages and kids, I will be able to claim prostate trouble and pee on their floor. Paybacks are......... Heh, heh, heh.