You might also cut a template from 1/4" MDF (or acrylic for that matter, whatever you have laying around) using your laser and use a router with a template-following bearing guide. Depending on your bit, you might have to stack a couple 1/4" sheets.

Might seem like a lot of work for cutting a circle, but I mention it here because doing things this way would open up some possibilites for doing other non standard shapes. Ellipse, round cornered rectangle...

Plus if you use the right bit (up or down spiral, depending on your use) you might have a good clean edge. A down spiral might keep the finish from fracturing or lifting up.

Shaddy

David,

You've been offered a lot of good advice, and here's one more suggestion:

Use a variable speed drill and drill at the lowest possible speed. Bit should be creeping. Very light pressure. As you pointed out, heat is the major culprit, and slow speed with light pressure will reduce that.