Thanks for the suggestion, Bob!
By "flush the engine" you mean drain the oil, and then pour some more straight through with the drain plug out? I'm due for an oil change soon, so I'll try that. I actually heard the same kind of noise coming from my '87 Taurus when it was low on oil. Maybe there's some kind of crud stuck in there.
Update: It's definitely temperature-related. Our cold spell here in Michigan broke a little, and as the car warmed up faster, the noise went away faster as well.
I don't want to admit that I need a new engine or something. Anything but that! I take too good care of mine!
