Is this the spec for the charger?
"Fully Automatic - Designed to maintain 12 volt batteries up to 250 amp hours
Increase Performance - Precision regulated 13.4 VDC float mode. Can be left on for extended periods without overcharging or damaging batteries. Will not drain battery if AC is removed. LED status indicator. User adjustable for gel's.
Built-in Safety - Reverse polarity protected. Certified to U.L. 1236 Marine."
Id leave it connected to your battery bank for a while longer and see what happens. If its regulated, you should be able to leave it connected and forget about it. Getting very hot should be watched carefully but it may just be that the "little" charger is trying to bring 500 amp hours of battery up to charge (which exceeds the spec) and they may have been low in the first place.
The one thing which I would be slightly worried about is temperature. The charger looks like it may not have temperature compensation and battery charging voltage's are temp sensitive. They need to be lower for high temps, higher for low temps. I would guess however if your batteries are in your garage or similar, no matter how cold a place where you live, you likely wont have a problem.