Computer crashes while playing games

Alright so I don't know where to start or what information to put so I'll do my best .

I got this computer (it's a laptop) about 8 months ago. Its a gateway nv57h13h

I have a intel 7 2670QM and an Nvidia GT540M with 1gb and 8gb of ram ( I don't know what to put else here :/) here's the link to my computer:
http://ca.gateway.com/gw/en/CA/content/model/LX.WYD02.004

Anyway, when I got this computer I would play league of legends for hours straight no problem ( it would get a bit hot on the left side where the fan is but nohing more)
Back in october my computer started closing down in middle of games and I thought nothing of it.
A month ago my harddrive broke ( deleted a partition and it went crazy) and I sent it to Acer and they reformatted the computer and I got it like if it was brand new (everything up to date, etc...).
But it still shuts down. Now I play League it closes A LOT, I just got BF3 and my computer runs it really smoothly on low and medium setting but 10 min in it just shuts down.

By the way I tried to open my case to get to the fan, I wasn't able to so I did it through the case as you can see the fan.
Anyway any insight would be awesome, I'm just exasperated by this computer

Looks like a nice laptop. "By the way I tried to open my case to get to the fan"... You didn't damage anything did you? Make sure you have All the Windows Updates including all the optional updates installed. I doubt if ACER did this at all... You sent a Gateway laptop to ACER for repair?

Yeah, its acer that own gateway ( I think but it is affiliated with acer for sure). And I tried to open the case I couldn't take out some screws so I gave up :/. I have all the updates of everything. I tried running games with icepacks under my computer and ofc they were evenlopped in a rug haha ( just to see) and it lasted about 30 min longer.

That wont really help at all... the effect of convection will be minimal. Are you running 310.90 drivers? Clean install them by choosing custom install: http://www.geforce.com/drivers/results/55125

Sounds like the CPU and GPU chips need new clean thermal paste and/or pads installed

Isn't the PC only a few months old though? I guess you must use it strenuously. If you need to purchase thermal paste get this:
http://www.amazon.com/Arctic-Silver...1&sr=8-1&keywords=arctic silver thermal paste

If it is still under warranty replacing the thermal paste will void any warranty. This kind of repair requires someone that knows how to repair laptops well

Ahh right I completely forgot that this was a laptop.

No problem, I've done this too... and I do repair all makes of laptops