Oooook, as others may have said, going thru the official route will probably work out best for you, BUT it can take a while, depending on the severity of the problem, where you live and the number of units theyre working on... (they have sites in kentucky/texas)
The towel trick CAN work, but can just as easily make things worse and is not recommended.
Sometimes giving the console a few days break will work, but the first thing anyone should do when they get the ring is check all their A/V connections. Check their power supply (brick), and that it has enough access to cool air to function effectively.
NEVER OPEN YOUR 360's HOUSING - This voids the warranty and dooms your console forever. The chances that you or anyone can fix the problem is slim to none, so dont even try.
I'd seriously just call MS support 1-800-4MY-XBOX, unless you have the $$$ to get a new/refurbed console... its the best way