Computer Freezes everytime I load in to a game

So I have a ThinkPad x1 Carbon and granted it isn't anything special, but its not a piece of crap either. That being said every time I load in to a game of league with in 2 minutes of being in the game my computer freezes completely and I have to hold down the power button and shut it down. This could be a graphics card error but I am doubtful considering I have played several more system stressing games and none of the other games had this problem.