Allan, you're right, but you're saying it backwards.

When a battery is stone cold, it's less chemically active and its resistance is higher. It imposes less of a load on the alternator.

Because the alternator has a lighter load, its voltage climbs and the system voltage climbs.

But when a battery is warm, it's more chemically active and its resistance drops, conducting more current. Because it conducts, or draws, more current, it loads the alternator more heavily -- and the alternator and system voltage drop.

And when the battery is fully charged, it passes less current, so its resistance rises and it loads the alternator less, just as when it's cold. The system voltage rises.

The alternator is not smart enough to know the battery temperature and adjust anything to compensate.
--
Don Foster (near Cape Cod, MA)