I can only quote Thetford's own manual whch states that the fridge should always be cooled using either Mains electric, or gas. It also clearly states the freezer compartment is unsuitable for freezing food, it will only keep pre frozen food in that state. That is a bit curious as it will make ice. The 12 volt system will only maintain the temperature if the engine is running. This means when the engine is off, or at idle the fridge is technically defrosting, and is not expected to 'catch up' too much. I have always found that if it is very well cooled prior to the trip, and the door is not opened, then it will survive quite a while, but I am sorry, I have yet to see a 12 volt device that will freeze. Any 12 volt in-car fridge I have seen always states that the maximum temperature drop that may be expected is 18-20 degrees below ambient. That means if you are in the Med and the outside temp is 35 degrees then your fridge will get to 15 degrees centigrade. That is not freezing.
Thetford don't actually give the power ratings for 12 volt but for 230 volt the unit is pulling nearly 12 amps, which is a lot higher than what you would hope to get from 12 volts.
Like any freezing device it depends on the ambient temperature. Thetford use a 25 degree C value which is fair enough, but will be insufficient in the Med where you really need the thing.