I'm looking at replacing the cpu in my ASUS N53SV i7 laptop possible upgrade?

Should use the existing i7 2630qm or can replace it an i7 2820qm if the cpu is removable from the mother board.

I'm looking for an answer from people with technical knowledge as I know a little about computers but not enough technical knowledge about motherboard compatibility for laptops as the two processors are fundamentally similar to each other on paper. Thanks in advance.

Laptop is 4-5 years has 2gb Geforce GT 540m, i7 2630qm cpu, 8gb of ram, 750gb 7200 Western Digital Black hdd

The cpu is running at mid 90's.

I was able to play Battle Field 4, Farcry 3 and Minecraft up until a month ago as the game will run for about 4-6 minutes and then shut itself down.

Looking for a cost effective option until I can save for a desktop system.

On some laptops it is possible to upgrade the CPU if they are socketed. However it may not be advisable, often the laptop has to be completely dismantled to get to the processor and you risk damaging many of the delicate cables and connectors if you are not used to doing this sort of thing. Also you may be running the laptop outside of the manufacturers intended specs, so a faster processor often generates more heat so the fans may be working harder and more noise, the battery life will be less if there's a higher power draw, the BIOS may not recognise the different CPU.
Most laptop CPUs are not sold direct to the end user only to the trade or manufacturers. As most of these CPUs are not current, then you would have to source off eBay or amazon. Finally most workshops would refuse this sort of work as you would be taking the laptop outside of the recommmended specs.

Have you thought about running an SSD instead of your HDD this will dramatically increase performance. Wouldnt bother doing the cpu upgrade will be expensive, not really a worthy upgrade. Change your HDD to an SSD

The CPU will be welded / glued / stuck into place. It won't be possible to change it.
The new cpu might not fit the space.
The new CPU might cause the laptop to overheat and therefore run slower.

CPU isn't going to do sh*t for you as it is not the main factor for overall performance - and definitely not in gaming.

So get that idea out of your head. As long as you have plenty of RAM, a good SSD, and keep the OS clean - that is the best you can do.

If its shutting down due to overheating - clean out the air vents, get a laptop cooler, or if you are feeling ballsy - open it up and replace the thermal paste, then clean out the fans/vents.

Other than that - you're screwed