The last time I did this I burned up my circular saw, or more
specifically, the brushes. I cut four doors that day, in fairly quick
succession. I'm no genius with a circular saw, but I thought I had done
it right. I used a fence as a guide and set the blade to protrude maybe
a half-inch below the bottom of the door. I tried not to go too fast.
This was a year ago, by the way.

I've since replaced the brushes and the saw works fine. It's a
pedestrian Skil model and has a fairly coarse 7-1/4" blade on it. I've
also got a much older saw with a 6-1/2" 40 tooth blade. I have another
brand-new HD solid-core door to cut down. It's the thinner variety that
they sell, 1-1/4"?

Tips, besides having an extra set of brushes around? Something to coat
the blade with to reduce friction, maybe? Cutting half the depth first?
(That doesn't sound like a good idea to me, but if you're too afraid to
ask, you don't learn)