Anders,
It sounds like the temperature control is the problem. Try disassembling and looking for bad, burned, or leaking components by visual inspection. If there are any bad capacitor you might be able to find them by looking for leaks. Otherwise, i would suspect the entire temperature control circuit. It's possible the sensor itself failed. These are usually a simple thermistor and easy to replace. Not sure about your model, but if you post some pictures maybe we can help better.
Best of luck