Watts anti-sweat mixing valve.
Since the problem toilet is on the 2nd floor, it poses more of a problem. To install an anti-sweat mixing valve, you have to have access to a hot water line, and a way to pipe the outlet of the mixing valve to the toilet supply. If the toilet is next to a vanity, you can install the mixing valve under the sink and run a new toilet supply out the side of the cabinet. The old toilet supply can just be shut-off and left where it is, or capped in the wall (in which case you'll have to patch the wall).
Another option is to get a toilet with an insulated tank - usually a styrofoam liner inside the tank. They sell retrofit liner kits, but they don't seem to work very well.
Finally, your flapper may be allowing water to leak into the bowl which means there's a constant/steady flow of cold water to the toilet. You may need to replace the flapper. This could explain why the first floor toilet doesn't sweat, but the 2nd floor one does. (Either that or the 1st floor toilet has a mixing valve, and the 2nd floor toilet does not).