My pots have plastic(?) handles which I'm sure would melt.

Only thing I've run thru self-clean cycle has been cast iron... stuff I picked up for a song with someone else's schmutz on it. The crud was reduced to ash... quick rinse, reheat and reseason.

Using high heat on enamel-coated products will eventually ruin them, the coating cracks and falls off. We made the mistake of using the foil-method to clean the grates on our expensive BBQ grill (after using the grill, you put foil on the grates, close the lid and crank the thing up to high heat for 10-15 minutes). In about a year, the grates were unuseable.

I'd recommend not doing the oven self-cleaning thing on your enamel-coated pieces on a regular basis. Cheaper and safer solution? Buy a lemon, rub the cooked on gunk with the cut side of the lemon, let it sit a bit, then wipe and rinse. May take a few applications, but it's an easy way to clean--even works on burnt on stuff in the oven. And the nice thing is? Lemon's both non-toxic AND smells so nice while you're cleaning.