Thing is the TC motors don't run any hotter but they have bigger cooling fins so they disburse heat better which means you get hotter, part of the problem is solved by reducing the inner temps of the motor.
It's running fine, it's just too hot for your tastes the temps you're at now are probably within the design of the motor. To reduce them to something that will make you comfortable is the option.
Do it one step at a time. Change the oil to Mobil 1 synthetic auto oil 15W-50 in the motor only, do not put it in the primary. This should reduce your operating temps 15 to 20 degrees, and it's cheaper than HD Syn3 and it's probably less than your dealer is charging for HD 360
If that takes care of it, then you're good to go,
The other thing, do you have lowers on the bike? If so you should remove them in the Summer, this is common on a lot of my friends baggers, they take them off in June July and Aug, or some company offers a set of flip open trap doors that go in the lowers to allow air into that area.
Finally check into HD's oil cooler if all else fails, you could also go stage 1 and get a bit more performance and drop on a DFO or powercommander to add some fuel and that will cool the bike down.
But start with the Mobil1 it might just cure your problem and certainly won't hurt.