Hi William,
You shouldn't need a MOSFET to run these motors.
Also, its pretty hard to 'burn' them out as they self-protect themselves pretty well.
However, electrically speaking, any gun with a 'micro switch' such as guns made by ARES are notoriously bad for having trigger switch bounce. Though it won't fry the motor itself. It may cause it to switch itself to 'SAFE' Mode.
All warhead motors feature a 'SAFE' mode. It basically renders the motor unuseable. To switch it off from safe mode, you need to manually plug in the wires directly to a battery for ~5 seconds until it spins again. Theres usually a red warning light on it if its activated while plugged in.
Safe mode only activates under the following instances, the motor detects a massive electrical spike (like a short circuit), the wires are plugged in reverse polarity, excessive PME strikes (also spikes in current), voltages over 12.6v is detected.
Overheat protection exists, which temporarily disables the motor until temperature falls back to acceptable levels.
So again double check the issue, and you might want to see why the motor reacted first. You may have a larger problem with your gun.