High output means high exhilaration! Try wearing some depends undergarments to mitigate the "wet spot". Seriously, I've said it before and will say it again (I know because I own an FJR).....FJR stands for "Food Just Right"! Simply place an uncooked burger near the heat source and by the time you arrive at your destination, you'll be ready to eat! It's all very simple you see!?
I had an '05 FJR. My solution was to finally sell it. Absolutely unacceptable. Big, hi-performance engines don't have to put out big heat. My 'Busa didn't make any uncomfortable heat. My ZX14 is hot, but nothing like the FJR. That's just poor design. They should be hung from their toes and flogged.
Yes, I think the ST is rather warm. However, many more don't complain about it. Perhaps Honda may have to abandon that design. That transversely mounted 4 sure throws a lot of heat back to the rider! Regarding the 06' fjr, you must be kidding - MCN proclaimed the heat problem was fixed for good.
If the seat appears capable of having something stuck to the underside, grab one of the smaller DynaMat kits with heat shielding. Beyond that your only solution may be to create some sort of ducting to direct air underneath the seat.