Emissitivity of copper - Why are copper heatsinks all shiny?

Radiative heat transfer is not dominant at the temperatures at which computer/electronic heatsinks operate, so the emissivity of the heatsink fin surfaces is not important for their operation.

Conduction of heat from the copper to the air, and then convection driven either by buoyancy or mechanical ventilation, is the dominant heat transfer mode that heatsinks exploit.

This makes the cleanliness of the fins far more important than their emissivity, which means anything that maintains them in a dust-free state will enhance their operation. This is why heatsink fins are made as smooth as possible, and not rough, and why the fan intake will have a lint filter on it.

The oxide tarnish that naturally forms on exposed copper fins at near-room temperatures is far thinner than a thousandth of an inch and therefore has a negligible effect on heat transfer. People who polish the oxides off to "improve" heat transfer are misinformed.