Major in-game FPS crashes or is my computer just breaking?

The title about says it all; usually in-game, I'll have major FPS crashes that last for a bit more than a minute or so before disappearing and the game plays normally again.

Now, my computer is far from the best, little surprised it can run League as well as it does. I'm sure my computer is just breaking in regards this mostly only happens during PvP game, when there is a crap ton of shit literally spewing across the map. It makes the game look great, sure, but half the time who knows what is happening during a team fight now'a days actually? 'Specially with the new Taric ult. x3 "Blind them with beauty!"

Point though, while I feel this is an over heating problem (yay!), I have heard other peeps mention in-game they've had similar FPS crashes as well? So I figured I'd pop on down to Boards and question the problem before jumping to conclusions. Am I going to finally have to fix my other computer or is there just yet another problem happening with the client?