It could be both actually, it could be a overheating problem, but I doubt the screen would make it shut down, so it has to be something with heat.
Start the computer, press DEL or F2 repeatedly as soon as it is turned on, the BIOS should load, go into the options and look for something to do with sytem temperatures, look at the temperatures and post it here.
It could also be that the graphics card is failing or has failed.