I would guess that the thermostat is broken and is allowing the fridge to run almost full time. An empty fridge is not going to be that much cooler than a full one,once all the food is cooled down.
I'd question the accuracy of your measuring (without knowing specifics) as most folks are unable to obtain that temperature with their absorption refrigerator. 30f->40f degrees is typical, some having difficulty reaching -40f from ambient. Have you tried placing a container of water in the fridge? A glass of water should freeze within a few hours at those temps you are stating.
