Drosophila - The Vermiculturist's Bane

I have also had a fruit fly plague -- they're really hard to get rid of. As to the compost, I have no idea what's wrong (temperature, moisture, if you're aerating enough). But in general to get rid of fruit flies, first you must get rid of the source. That means any open garbage, or fruit, veggies or other sweetish open foods. Keep it covered (you may need to trash your curent batch of compost + start over). Then, the best fruit fly trap in the world is to put apple cider vinegar in a jar and cover the top with saran wrap. Poke a few holes--flies will fly in but they are generally unable to fly out and they drown. Change the contents after a week. It takes a week to ten days for fruit flies to die, but the larvae can fly out of a jar so you don't want yr flies mating in the jar.
You MUST get rid of the source to get rid of flies. One tiny gooey bit of banana behind the toaster and you're a goner.

Hmmm. Well my kitchen could pass for an operating room, so that won't be the problem. Ironically enough, the flies really congregate around the bottle of dishsoap. I had to start keeping it in the fridge.

As far as the composter... moisture and temperature are both in check, maybe I'll try aerating more. If that doesn't work, it sounds like burying this batch in a friend's garden and starting over is the thing to do.

What do you use for bedding? The first bin was hay and the newer one (which seems to be worse for flies) is mostly shredded newspaper.

Making sure there's lots of newspaper to keep the fruit well-buried helps keep my flies down. And I second the apple-cider vinegar traps suggested above.