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