OK… one fridge duly repaired. Looks like the thermostat (a very simple device that gets stuffed into a little hole and plugged into the circuitboard) had fried itself.
The little silver metal thing on the end can rotate all the way round, like a child’s head in a horror movie. The new one has more backbone, and cannot rotate at all – I assume this is a “good thing”. All in all, a simple (if disappointing in the first place) fix. The fridge is currently in testing with a load of beer, but things are looking good (its down to 5 degrees, from close to 30 when we began…).
It is still going home to NZ in the other car, where my brother has kindly volunteered to keep it gainfully employed and full of beverages.