Ps2, overclocking takes patience and understanding in order to do it correctly. First a little bit of reality for you, your board isn't the best platform for overclocking on with a FX chip. We have found that these new processors need a lot of clean power from the VRM section of the motherboards in order to be stable when overclocked. You board, as Wipeout pointed out, only has 4+1 power phases in the VRM section. This may cause issues for you when overclocking and we will cross that bridge if they arrive. Second what 600w PSU do you have, it does make a difference.
What I feel you should do is lower your clocks to say 3.6 and then test prime for 2 hours, make sure your temps on the cputin stays below 70c and the package temp below 60. If you can pass 2 hours then bump the multiplier up and run it again, if it fails in any way you need to increase the V core 1 notch. This is where the process takes patience. Is it a pain to just sit an do nothing waiting for 2 hours of prime to run in order to see if it's stable, yes. This method works though and it is worth it.
If you really want to get a new heatsink the CM 212 + is a good low cost heatsink but you may find your board cannot handle the overclocks before you even run into temperature problems. I would worry more about getting it stable and then see how far you can take it, keeping the temps in check before you go buy a new heatsink.