lol. it's not just a fan, it's a fan on top of a heatsink. Which together makes a CPU cooler. Because, you know..... it cools the CPU.
But if you're using the stock cooler, I also assume you haven't even bothered to overclock your CPU?
A question I would now ask at this point is this:
Were you foolish and purchased this K series CPU without also pairing it with a Z series motherboard?
Hopefully you have a Z series motherboard that way you can overclock.
As for upgrading to Windows 10 the answer is yes. In general it's better optimized for gaming than W7. And on top of that, Microsoft isn't supporting W7 with updates anymore, so it's a good idea to upgrade for security and system stability reasons as well.
When it comes to overclocking the 2nd gen Intel chips, there's a fairly specific way of doing it.
Refer to this guide for help.
https://www.overclockers.com/forums/showthread.php/693613-Beginners-How-to-set-your-25-6-700K-to-4-5Ghz
Be sure to read thoroughly and carefully to fully understand what it is you're doing.
And it's possible there is a thread made for overclocking that CPU on your specific motherboard or it's family as was the case with my 2500K and an AsRock Pro3 Z77 board I had back in the day.
Also note, that when removing a cooler from a CPU to put a new one on, be sure to carefully and completely remove all the paste that is on the CPU before putting the new cooler on.
While the paste that comes pre applied to the 212 Evo is OK, you could do better if you like.
On a budget, I would suggest some Arctic Silver 5. You can usually get this in a 2-Pack for fairly cheap on Amazon.
When applying your own thermal paste, be sure to also clean the pre applied paste on the cooler, then squeeze out a pea sized amount of paste on top the CPU right in the middle then proceed to mount the cooler and tighten it down by doing opposite corners and not fully tightening each corner but doing them more equally all around until they are all snug as a bug.
Refer to the plethora of YouTube videos on such things if you need more of a visual.