Why is my xbox randomly turning off when playing games

I am an electrical engineer and see this all the time. The problem is that the heatsink and fan aren't large enough to handle such a change in temperature in such a short amount of time. The best way to repair this is to use an old Desktop (High Power) Power Supply. Change the Fan to a higher current 12 Volt type, remove the old thermal compound, replace with new and add as much metallic heatsink as possible. The power cord for the Xbox has 5 conductors. Red, Black, Yellow, Green and a Shield. The Red wire is positive 12 Volts, Black Wire is Ground and Yellow wire is positive 5 Volts. Cut the Green Wire and Shield out, they're not needed. I've taken the plastic casing off of my Xbox and even added heatsinks to the bottom of the metal chassis along with more 12 Volt Fans. Anything that can remove heat from the main IC without shorting the pins on it will work wonders. You can also try and do a SMT Reflow as well in case some of the soldering has become brittle. This is a delicate process and you can damage the BGA and other smaller SMT Quad pack chips if not careful so be sure to research this before trying.