You don't even need to spend that much :P To be honest i hit 3.9 by switching my thermal paste from AS5 to IC7 (FREE!!!
) And i had a 40$ cooler (the V8). The best cooler is the Hyper 212+ for cheap price only 25$ on Amazon. Stick two high performance fans on it and let it rip. It'll run you cheaper than a frio or a Noctua since even two 20$ fans on the Hyper 212+ will still be 65$. Or you could stick with the stock fan and just spend 25$. http://www.guru3d.com/article/cooler-master-hyper-212-plus-review/7
As you can see it compares with 70$ heatsinks for only 25$. Also, once in dual fan it'll perform even better. Plus the saved money can go towards a graphics card upgrade or (if it comes out) the Zosma a Phenom II X4 with two dormant cores that are possible to unlock.