Once you have homed the printer, the enable signal of the driver will be on and the driver will get hot. Some firmware have options for switching off the stepper after a few seconds of idle time or at least reduce current to the motor.
But it is still a good idea to cool the controller, since there are other components getting hot too ( 5V regulator, CPU )
But it is still a good idea to cool the controller, since there are other components getting hot too ( 5V regulator, CPU )