I have a 2007 FLHTC and have experienced the same issues. It was very intermittent and was checked out by a HD dealer while I was on a road trip and they could find no issues on the check out. Brought it home and within a week the voltage regulator when out and was replaced and took care of the issue for about two years when it had to be replaced again along with the stator.
The first year 96 cu. in. ran extremely hot and was told to not use the chrome cover so that more air flow could help keep it a little cooler.
Ride Safe