The 2007 models had an optional temperature management system that would shut down the rear cylinder at idle when the engine temperature (head temp, not oil temp) reached a certain point. When it does that, the exhaust note will change dramatically, possibly similar to the "air coming from the back of the engine" that you mentioned. It also wasn't totally uncommon for the system to not work quite as well as Harley intended, with stalling or hesitation when you first attempted to open the throttle. I have no idea if your bike has had this system enabled or not, but a dealer can tell easily by hooking up to your ECM and checking the calibration number.
As for the throttle being hard to turn, that could be related to several things. Overheating to the point of actually melting the sheath of the cables isn't likely unless the cable was lying directly on the head, but it is something to check. You can also try adjusting the cables for maximum slack and then operating the throttle plate by hand after removing the air cleaner. That will tell you if it's a cable or grip problem versus a throttle body problem.
In the future, if you need to let the bike run in the garage for more than a few minutes, I'd recommend setting up a large fan to blow air on the cylinders and heads. Modern Harley engines will overheat rapidly without adequate air flow, even if the outside air temp is low.
Jerry