Why does my computer lag on every game i play?

ok so not that long ago i was just playing starcraft 2 and i have it on the lowest graphic settings and it just starts to lag after 5 to 10 minutes and then it will last for a few minutes then go away and come back. I got an error one time and it said my graphics card shut down but the error hasnt came back since. I tried a few other games and the exact same thing happends, so if you know whats happening here please help.