It's probably not the monitor that's the problem, if it works otherwise, although there is a small chance that it could have a thermal fault. You'd have to try a different monitor.
More likely it's that your video card is overheating. In any case, the first thing to do is to open the computer up and make sure all fans are running and then shut it down and clean the dust out of the computer, particularly any heatsinks and/or fans.
If that doesn't help, it's most likely that your video card can't handle the graphics settings in the games. Make sure that your in-game rez matches your monitor/desktop rez and lower the settings level.
Last edited by Quaker; Dec 02, 2011 at 07:32 PM // 19:32..