I really deosn't make much sense to have a copper heat sink where you have enough space to use aluminum. The speed of heat transfer increases when either the the medium that the heat is transfering through is more heat conductive, or the crosssection increases.
This is why you will often see heat sinks that are thick at the base but tinner near the top. You can get the same effect of an copper heat sink by using a thicker heat sink. Aluminum is also easier to cut and is cheaper.