This happened to me too and the short term fix was indeed to press the small red button on the back.
That button is a thermal overload trip. Its job is to trip when the machine gets too hot *and alert you to the problem*. It is important that you find the reason for the overheating and fix it properly.
There are lots of possible causes of overheating. On my machine it turned out to be that the temperature sensor on the back of the drum which switches the elements on and off to keep the heat constant during the drying cycle had disintegrated - it simply fell apart in my hands as I was examining it. Crosslee sold us a spare relatively cheaply.
Calvin
January 2005