Servo motors...
The reason that I askd if the stab motor was a servo is that servos behave differently to the normal motors we are all used to. They were developed for cnc machines...they accurately will move about 1/4000th of a revolution per step signal, and then lock their rotor. So they need a command to move x steps in Y direction at whatever speed. That can be a simple analogue instruction; run clockwise at speed number 3 until the limit stops are reached.
But it would make more sense for the FCC to signal a step + direction command. However many steps to get 2.5 units of nose down trim.
The critical feature is again the locked rotor when not turning. If the clutch doesn’t work, or doesn’t work well, a human will not be able to move the rotor from its last commanded position.
I have had four big servo motors in my garage machine shop so am quite familiar with their characteristics.
I am also a 737 pilot, and have had a failure of the stab trim brakes in flight...a soft runaway requiring cranking the wheel. It wasn’t a big deal, but then again we were smack in the middle of the envelope, and the -400 had a both a shorter moment arm and a 10% bigger trim wheel to crank.
Regarding motor overheating: I really doubt it. I have run servos in 45° heat with a big load running constantly for a couple of hours relying only on their passive air cooling. Never had a thermal shutdown.