[JRTJH]

I think the OP's question has as much "hidden considerations" as it does "visible considerations". If you think about it, his 2011 Cougar 327 has three slides, electric front jacks as well as the furnace that all run on (are powered by) the battery system. So, if all he has is a GP24 battery, he may well be at "half power" by the time he gets unhitched and the slides extended. That would be a "VERY COLD NIGHT" once he crawled into bed with the thermostat set on 70F if he were depending on what's left in the battery.

So, if travelling and not deploying the slides, he might "squeak by" for one night "IF" he didn't use much in the way of lights, didn't shower (water pump use) and didn't rely on the battery for any entertainment use (TV or radio). On the other hand, if he unhitched, levelled the trailer, deployed the slides, extended the awning to relax a bit, then cooked supper, washed the dishes, took a quick shower and sat to read a book for a bit before bed, there's a good possibility that the lights will be dimming by the time he adjusts the thermostat and turns out the bedside light. He can pretty much forget about retracting the slides come sunup. On the other hand, if he is dry camping, has a generator to recharge the battery, doesn't use the slide motors, awning, water pump, etc, then he may get through the night with the battery providing power for the furnace.

So, the answer to his question, 'will the battery run the furnace all night?" has more to consider than just the furnace fan motor "battery consumption".