Just to add my bit (
), EB has pretty well got it (addressing the original questions). With nothing plugged in, there should be NO current drain. The only way you could have a current draw is if there's a wiring fault, which would mean a short circuit. If you had such a s/c, either the fuse would blow (which is what it's designed for) or the wiring would melt. Either way, you would not have a constant, steady current drain.
As for running a GPS, their current draw is pretty low, and would be insignificant while the bike is running. If the dealer is trying to tell you that is what's happened, one would have to question said dealer's qualifications!
And I cannot see any way on earth that the circuitry in question could have anything
whatsoever to do with the bike overheating!!
Has the dealer suggested this, or are you merely trying to rule out possibilities?