The degauss is "hard wired", that is it does it's job at every power on. A thermister works as a timer of sorts. The degaussing coil is energized, and the thermistor heats up until it reaches a certain temperature, then it shuts off the relay to the degaussing coil.
The degaussing is an important thing as the CRT uses a deflection yoke, which is basically an electromagnet to deflect the electron beam to draw the picture on the face of the CRT. Since this is done electromagnetically, you must degauss the CRT to prevent "purity" issues caused by the magnetic field of the earth (no joke).
The earth is itself a big magnet. the North pole is actually the south pole of the magnet, and the South pole is the north pole of the magnet. Lines of magnetic flux flow between the poles, affected by the sun and the makeup of the earth itself.
If the CRT doesn't degauss, you will soon get colors in the corners, and eventually over the entire screen (think 60's flashback). You can see the same effect by moving a magnet (an unshielded speaker for instance) close to the CRT. Or if it is a large CRT, move it's orientation (turn it 90 degrees, etc).
PC CRT monitors also have a very fine pitched aperature, which can warp if not degaussed, causing incorrect beam landing (colors where they shouldn't be).
Long story short, let it degauss, it will only be for a moment, and it will save your CRT. It isn't something that can be turned off in most cases, as the manufacturer wouldn't want the CRT getting ruined prematurely. A Guy