To be honest you'd be better off with a new cooler... It will drop your temperatures and the E6300 is a beast when it comes to overclocking... Throw 1.4Vcore at it and you can hit over 3GHz with ease with a nice third party heat sink. Being in the high 50's is crazy...
Just curious, but is this an old Intel HSF you had and a tray processor or was this a retail processor in a box?