Condensation on your toilet's tank can cause serious problems with your floor. Just like having a glass with a cold drink in it sitting on your wood furniture, your toilet is filled with fresh cold water every time you flush. This rush if cold water chills the toilet's tank and on humid days, can condensate. Excessive condensation will drip, causing standing water on your floor.
Since this toilet was already dismantled and I cleaned it with Barkeeper's Friend the day before, I decided I would attempt to insulate the tank. I've never done anything like this before and I can't find any other blog posts or anything with people doing this. I guess most of the rest of the country just blasts A/C from March 'til September.
I had some left-over fan-fold insulation from a siding patch I did a few years ago. I have been using it as floor covering to protect any installed floors when I work on them. The insulation provides half an R value - which should be about the same as a beer cozy - only on the inside.
I used some specially formuated glue for XPS. I think you can get XPS-safe glue in caulk form. This stuff attaches to your normal spray foam gun and comes out almost exactly like spray foam. It doesn't expand as much over time, but it does behave and cure almost exactly like regular spray foam.
To keep pressure on the rounded part of the tank to let the glue cure I put a bag of rocks into the tank. I figured they would be form fitting for the curve and heavy enough. I didn't do this for the flat back and bottom, but if I had to do it over again, I would cut all the pieces and glue them all at the same time and maybe put a garbage bag full of rocks or water in the tank to apply pressure.
The insulation doesn't have perfect coverage, I'm hoping that's not a problem. If I see a few thin lines of condensation I'll drain the tank and re-apply the inuslation.
Other Methods
Fan-fold insulation is hard to come by. You have to have purchase a giant stack of it, enough to do dozens of toilet tanks. Using something like half-inch XPS board might be too big to fit in your tank, and you'd still have a lot left over. You could buy a a whole package of fan-fold and just throw the remainder in your attic - you can never have too much insulation in your attic.
I saw a video on Youtube where one guy was using a can (tin) of spray foam and constantly sawing it flat and reapplying more spray. This was to get a uniform, unlumpy thickness. This sounds like way too much work because you have to wait a few hours for the foam to cure and become saw-able.
I just found that some people sell foam kits to do this same thing, so it's not as crazy as I thought it was and you don't have to buy too much insulation. Although, fan-fold does come in handy for protecting floors.