It takes more than three weeks. At least, it did for me.

If you REALLY don't feel like sending it to MS, you can do the towel method (but I stress that it's only a temporary fix; what I would do is call MS, wait to receieve your box, and do the towel method while you wait)

1. Wrap your 360 in a towel, and cover all of the vents.
2. Turn on the power, and leave it on for about half an hour.
3. MAKE SURE you monitor it, and if it gets too hot, or spazzes out, take the towel off. No need to start a fire.

I have no idea how this works, it has something to do with melting something that's inside.

Either way, it works for a few times.