The Eggbot motors use a similar amount of power whether or not they are turning, since the coils in stepper motors are continuously energized whenever power to the motors is turned on.
If the motors are getting excessively hot, you may want to adjust the motor current down. There’s a “sweet spot” in terms of motor current, where the drawing quality is best (not too much current, not too little current) and the motors tend to run at a reasonably-warm medium temperature.
From what I can tell, also good to make sure your motors are really idle (ie: easy to turn) and not locked and standing still. If not easy to turn, pick “disable motors” from the eggbot control manual command.