Problem with fan motors is that they depend on the air from the fan for cooling... remove the fan and you may have problems...
.... not necessarily, a lot of the air a fan blade pulls in doesnt even contact the motor. they can run for a long long time in super hot conditions and not even blink. ie 110+ for 24hrs a day. for i don't even know how many years. and the only thing that bats an eye and goes bad is the start/run capacitor.
also if the motor has no rear fan blade for air movement you shouldn't have to worry too much about it overheating unless you are putting an external heat source on it, they will be built from the factory to take a beating.
i've got about 10 single phase .5 and 1hp motors from various things (mostly fans, some tossed and completely new baldor motors) at work and plan to make a few nice shop tools like a belt sander setup, disc sander, etc. not to mention having a bunch of super nice industrial shop fans to move air when working .