I thought they fixed that with newer versions of the old white 360 (mine is a newer white one with no problems), but I did read that the new one has temp sensors and warns you on screen when if it's getting too hot and will shut itself down if you don't do it yourself.
New XBox 360 Adds Long-Overdue Thermal Monitoring - HotHardware

But it also looks like you need to be careful not to move or bump your system while it's on (not that that's likely a common occurance.)
New Xbox 360 Packs a Mean Bite, Will Chew Your Discs if Moved - HotHardware