The 12V battery get its power from a dc-dc converter. There is no alternator.
What most likely happened is:
1) You never got up to temperature until about halfway home. This is very likely with your low speeds and no grill block, even without using heat.
2) You didn't stop long enough to enter the S4 warm up mode after you were warmed up.
Check out the stages of warm up here:
http://techno-fandom.org/~hobbit/cars/five-stages.txt