There are many 12 volt loads you may miss, like the propane detector, stereo, and fridge electronics. In addition to the furnace, fans, and lights that you notice.
Once the compartment the converter is in warms up (even though the outside temps drop at night) the heat out of the converter can be enough by itself to keep the fan on. Landing gear and slides pull a bunch out of the batteries when you are running, as well as the "missed" loads when traveling. The batteries may have ben at 80 or 90% when you were done setting up.
Is your converter loose, or integrated into the braker panel?