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Precisely! We do have to consider the practical side of it so it always comes down to copper and aluminium.. And using either of them with greater machining skills and designing is the better way to go..I've often thought that the whole aluminum is better at giving off heat vs. copper was a load of wash. However, I think the "truth" in the statement comes from the fact that the copper can store more heat due to its mass and SHC, so it doesn't heat up as quickly, and therefore it has more "heat inertia." The result would be that the mass of copper needs to absorb more heat before it creates a higher temperature gradient at the fins. Aluminum can't store much heat, so it heats up more quickly, which means there is a higher temperature gradient at the fins.
Ultimately, cost aside, I think using copper would be the best material for any heatsinking short of exotic materials, because it can both store heat, and transfer it. Aluminum would still be my choice as it cheap, conducts well, doesn't weigh much, and is easy to work with. It may also be good for having the host heat up more for a higher temperature differential at the surface.