Hi there, I have one of these vans as well and the house thermostat controls the heater below the last cupboard at the back. If your heater control is operating the fridge then something has been wired differently I think. Maybe others with thIs setup can shed some light. My fridge is controlled solely by the controller in the fridge it flicks automatically to 240v when plugged into the mains and when on 12v I have a separate switch that can turn it off or on near the battery although this is not standard it was installed by the previous owner. The fridge does cut out if the battery voltage is low though not sure what voltage though as the current battery is stuffed so wasnt running on 12v, I tested by hooking up a different battery and ran fine. Not that this is your problem but maybe your fridge needs a service?
Life is far too short and seems to get shorter every day!