There is a relay typically that disconnects the charge to the battery when the motor isn't running. If you are like me and prefer having a dead battery in your tow vehicle to freezing to death, you can replace the relay with a jumper wire/fuse (and carry one of those jump starters. This makes some sense as well as due to the resistance in the wires, the charge current is limited to about ten amps. This means that it pretty much takes all night to transfer the charge from the TV battery to the TT battery.
Another tip - before relying on a battery to keep you warm at night - equalize the battery, then equalize it again, until all the cells read 1.30 with a hydrometer.
