That's actually one reason to keep the OEM coolers. They are designed to work with the CPUs they come with where 3rd party coolers are "universal" and like most "universal" products, they make compromises to fit the most applications, and rarely are a "perfect fit" for any.
Studies have shown that heatsinks are more efficient when "turbulent" air is
blasted "on to" the heatsink as opposed to an easy
flow "across" the heat sink, which occurs with horizontally positioned fans.
As Titanic correctly noted, you did not tell us what model you are using so we don't know how your fan is oriented or which direction it pushes air.
Note too that many, if not most fans with DC motors only spin in one direction and reversing the power leads often results in no spin, or damage to the motor. But even if the motor's rotation can be reversed safely, it is important to note the fan blades are aeronautically designed like an airplane propeller and their shape (pitch, twist angle, blade angle, leading edge, trailing edge, etc.) are designed to provide the most air movement
in ONE direction only. Meaning, if you reverse direction of the rotation, you reduce dramatically, the air flow (CFM - cubic feet per minute) and heat extraction. This is exactly why most cooler and case fans have two arrows pressed into their housings; one showing spin direction, the other showing flow direction, as seen
Link Removed.
Note a ceiling fan. The blades are mounted at an angle, but the blade surfaces are flat so you can reverse rotation direction. But CPU heatsink and case fan blades have a twist in them. The are not designed to spin in both directions. So the proper way to reverse air flow on a heatsink fan is to turn the fan over (or around), not switch wire polarity.
Note the other main reason to use the coolers that come with our Intel and AMD CPUs is because using 3rd party coolers on CPUs that come with coolers, voids the 3-year CPU warranty! For that reason, contrary to false rumors by way too many, OEM coolers are excellent coolers. Perfectly capable of providing adequate cooling, even with mild to moderate overclocking.
Main issue is, of course, what temperatures your CPU reaches.
Exactly!
And lastly, it is important to note it is your case's responsibility to provide an adequate supply of cool air
flow through the case. The CPU fan need only "toss up" the CPU's heat into that flow. In most cases, you are looking for good front-to-back flow through the case. I generally recommend at least two large (120mm or larger) case fans, one in front drawing cool air in, and one in back pulling heated air out (not counting the PSU fan).
If you are not doing "extreme" overclocking and your CPU is not staying cool enough, look at adding case fans. The coolest temperature possible is not necessary. You just need to keep the CPU in it's normal operating range for it to remain stable. I get nervous when CPUs temps hit and stay above 60°C. Below that is fine.