Well, there could be a lot of reasons for the motor not turning when you send a pulse. Is it wired correctly? Are you sending it pulses too fast (if you try to make it turn too fast without slowly ramping up the speed, it can stall)?
You need to put a heat sink on the L298, because as you said it gets very hot. It doesn't have to be a fancy heat sink, though; I just bolted on a large piece of aluminum trim channel onto each of the L298's on my stepper motor controllers and that was enough to keep the heat minimal.