Do you have an owner's manual to see what the motor should be for your machine? One reason why the motor could be over heating is if it's too small and working too hard to power the machine. A smaller motor will only make matters worse if that's the case.
Do you have a HP rating or the amps used shown on the motors? Volts x Amps equals power in Watts. That will give you at least a rough estimate of the difference in power between the two. You will want them equal or the new motor to be a little more powerful.
If your new motor is twice as fast you want it's pulley to be 1/2 the diameter of the original pulley to keep machine speeds the same.
It won't hurt to try it and see if you already have the motor laying around but I think you would be better off finding a closer match to your current motor.
Rodney
*Jim beat me to it*