don't have access to e-mail at work so ill justt reply here.
since you mentioned it is an xbox 360 elite, i can safely assume it is at least 3 years old now and starting to give out on you. sound like the GPU is having some issues keeping cool. try opening up the console and cleaning it out and and apply new thermal compound to the GPU and CPU. I use arctic silver 5 which can be bought at just about any small computer shop, never found it at any big box stores around my place.
try that out and see what results you get, if it is still having issues then it could potentionally be the solder is going back and needs a reflow or a malfunction in the chip itself