It's basically a thermal resistor (posistor) that will conduct (turn on) electricity until it reaches a certain temperature/resistance and then it will "open" (turn off).
In your case it's the little black box right near where the degauss coil plugs in.
Best to check out of circuit... using an meter check for ohms/continuity across the two pins.
When cold it should give a reading, when hot it should be open. (not sure what the actual resistance is on that one)
You can also just unplug the coil and insert your meter to the two pins of where it plugs in and see if the voltage kicks up when you first turn it on. (set meter at about 200V AC)
A digital meter may not give an accurate reading because it happens so quick, but it's enough to know if it's kicking ON and then should turn quickly OFF. An analog meter may be more accurate on reading the actual voltage it's putting out.
Someone correct my layman terminology if need be please.......