the fuel regulator, it being metal I believe it is absorbing engine heat and when you stop I think its pushing that hot gas back up to the fuel pump
The fuel is circulating all the time the engine is running. The pump runs all the time and the FPR just keeps the rail at the right pressure. Anything 'over' is returned to the tank. The fuel goes through the pump, then to the rail, then the FPR and returns to the tank.
This is where some of the 'problem' comes in - the fuel is constantly picking up heat from the engine and taking it to the tank. If it weren't for the return line you would never get enough heat in the tank to notice.
It's not a regulator like you would use on a gas bottle (LPG/propane, not gasoline - just to clear that up), it's a bypass regulator, hence the return line to the tank.
Relocating the FPR and lines is certainly possible - put them anywhere you like, they don't care, they don't even have to be under the fuel level so if it
really bothers you put the FPR up on the 'bars or fairing to get some air around it.