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.
For instructions on how to adjust the motor current, see here: http://wiki.evilmadscientist.com/Making_your_first_plot#Drawing_on_your_Egg
