The fridge in AUTO runs first on AC, then if that is not available it switches to propane, then if that is not available it runs on DC. Inverter is not needed in this application. It is running on propane, since it is available. If you shut off the propane it would switch to DC or if you manual switch it to DC. However, the 3 way fridges are notoriously inefficient compared to your home fridge and will burn through batteries very rapidly. The best solutions are probably to leave it on propane, keep awning out if possible to shade the refrigerator. Keep the number of items in the fridge small enough that you can have good airflow inside (in otherwords don't overpack). I have also installed a supplemental fan to pull air through the coils to help efficiency.