First of all, you only mentioned a fan for your processor, a heat sink is also a critical component for today's processors. Without one, it can fry intantly.
But, before you install a new heat sink, or if got one on the processor already, make sure there is thermal compound!!! Arctic Silver 5, or other thermal grease should be fine. Check online for application instructions.
Now, if you already have all that, then you need to check how hot is your processor running. Usually Bios can tell you. If it's running above 55 deg C, it's probably too hot. An ideal processor temp is 35-45 deg C, and maybe 50 at full load. Although 60 deg C will not kill your processor either, but shorten its life span.
Increasing the amount of fans does not mean cooler PC, because of turbulance it can actually increase your processor temp. You should have 2-4 fans at the most depends on how big they are and where you put them. Depends on the case, here's a example:
One 120mm exhaust fan on the back of the computer, blowing OUT, draw hot air out.
One 120mm blow fan at the front of the case draw cool into the computer, blowing toward the back of the case.
If a side panel fan is present, it should be blowing at the processor, 120mm size desired, but most cases offers 80mm ones.
There can be a fourth one, it's called a blow hole, which is on top of the case, blows hot air out from the system. Depends on the case, you may or may not have one. It's not necessary, but it's cool.
Now, that's based on the 120mm fan system, if you can only fit 80mm fans, you may need more, which sucks because they are loud. That's right, when purchase fans, buy quiet ones for your ears' sake. Antec or Vantec both are good.
Well, it's long, but hopefully helpful.