I'm trying to track down the same issue. It's intermittent. Seems more common when it's colder, but has done it at over 50 degrees F. So far it has only done it after the car has been sitting over night.
Mine actually seems to start screeching while the starter is running, then stops abruptly less than a second after the engine fires up.
It's a horrifying noise....doesn't sound like a belt to me, but who knows.