Christian Stan explains how he solved this case in a post at Buzzle.com
A problem that comes with Xbox 360 is quite common and earned its own name from gamers, the Red Ring of Death. The name of this error comes from the red lights, which change from the regular green ones. These lights are located at the front of the Xbox console. The Red Ring of Death is the error that is usually caused by the heat which builds up inside the console.
The console produces heat as it’s operated. Heat sinks should dissipate the heat build-up, but they don’t always do their job. The solder used in the console is lead free, so heat can affect it in time, causing it to become brittle and producing hairline cracks. The cracks can break the circuits.
A red light that is flashing might indicate that a failure of the hardware has occurred, which can be caused by the processing unit overheating. You should put the console on a box, with plenty of free space around, so cool air can get to it easily. This way the chances of issues with hardware failure are greatly reduced. You shouldn’t put it in a TV cabinet or a cupboard, since the cool air wouldn’t be sufficiently available to the console and its cooling vents.
Sometimes, people confuse the red ring of death with another similar problem, which involves four red lights flashing. This error is caused by the AV cable, which isn’t plugged into the console. As soon as you put back the cable in the console, your problem should be fixed.
If your main problem is the dreaded Red Ring of Death, you might be lucky. Microsoft has an extended warranty these days, increased to three years, for the consoles that have this issue, as long as you haven’t opened the console and you’re the one that bought it.
You can also repair it yourself using a repair guide. There are great guides available, with video instructions on how to do repairs step by step, with some basic tools that you have in your house. The advantage is that you can repair a console in a few hours, instead of waiting a few weeks to come back from repairs.