Laptop fan problem -- too low?

Note: Best Buy fixed the issue a while back. I had to reformat since then, and my service plan is up. So I'd like to re-fix it myself.

This is the original problem: I'd had my computer (Asus notebook G73jh) for 6 months. Suddenly out of the blue, I couldn't play any game for more than 10 minutes without my computer overheating and crashing. Best Buy, quote, "updated the BIOS" in order to "fix the fan speed" and it seemed to do the trick.

So, fast-forward. Reformat. Start experiencing the same problem again. Update the BIOS version myself. ... Still happening.

If everything that I think is true IS true, then, I just need to do something with the fan speed. I can't find how to increase it. Everything I read on the internet tells me that my fan speed should already be maximized, which is why there is no BIOS option where you can tinker with it; the only thing I can find on the internet is people asking how to LOWER and quiet their fans. That is the opposite of what I need. I want to crank the sucker so I can actually play my games again. If you can tell me how, please do so. Thanks.

The laptop probably needs it's fan cleaned and the CPU/GPU thermal paste or pads replaced