amd fx-6300 stock cooler

The all aluminum FX 6300 stock cooler is terrible for any purpose. This is not an exaggeration. I've worked with several.

Look at the FX 6350 instead. For the $20 more you get a faster CPU AND a copper base plate + heat pipe style cooler like the one the 8350 comes with. Much better than the 6300's cooler.
 

beoza

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Probably if your case has decent or good air flow. But I would seriously think about replacing it with something better like the CM Hyper 212 EVO, Noctua NH-D14 or D15, or Phanteks PH-TC14PE if your case can fit them. These companies also make low profile fans that are pretty good and perform much better than stock coolers from AMD or Intel.
 


^ This ^ is also a good idea.

Just bear in mind, aftermarket coolers like those recommended above will be $30-$90 extra.