Most ancient HDD used stepper motors, which was ok because of the very limited number of tracks. Because of the fixed steps, they could get into troubles because of temperature variations changing the physical dimensions. The old drives with 80ms or 120ms seek time had very distinctive sound from the stepper motor.

A modern HDD with very high track densities is using a voice coil, allowing the head to move with high precision without being limited by the step size, or max number of steps/second. Instead of counting steps, the drive quickly moves the head to an approximate position and then picks up servo information for fine adjustment. Wries have a higher requirement for perfect tracking, so the seek time will be a bit higher for a write than for a read.

I have done some work with speakers, and haven't seen a problem with heat. The amount of power depends on how much deflection that is needed. But for a laser animation, you normally don't need so big deflection. A small cone movement can represent a very large angle change for the laser beam.