Silver (Ag)
Here's the thermal conductivity of a all materials: http://periodictable.com/Properties/A/ThermalConductivity.html - just put the mouse over the points in the graph
As you can see, silver is not much better than copper at transferring heat. It's not worth the extra price.
In addition, silver is a bit more malleable than copper, even more malleable than aluminum, which makes it not such a great choice for mounting it with pressure springs or some other mechanism that exerts pressure on the metal.
It matters less when it comes to heatsinks but aluminum is also way more ductile , see https://en.wikipedia.org/wiki/Ductility if you don't know what this means.
But really no matter what material you use for heatsink, the problem is not the material but the flatness of the two surfaces - the heatsink has to be super flat and the surface of the CPU has to be very flat as well which is not the case (manufacturers have to engrave the product codes on the metal lid, the lid itself has to be applied over a much smaller silicon die with some thermal paste between the die and the actual lid,and this lid is not perfectly flat due to how it's "glued" to the organic material which has the silicon die in the middle..
Anyway.. so even in a perfect world the actual material used for heatsink doesn't make a huge difference as long as it's one with good conductivity. A much bigger difference makes applying some kind of thermal paste versus not applying any paste at all - paste fills the microscopic hills and holes in the surfaces of the cpu and heatsink and makes things flatter, the surface through which is transferred to the heatsink increases and everything works better.

Besides the toughness and corrosion columns, for heatsink appliations in all the other columns it's not good to be on top.

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