shiny stuff refects light, and will probably also reflect more heat....so if your worried about the heat from the outside polished is good

and if you paint it then the heat will have to be transfered through the paint also....so less stuff on the outside of the cooler the better

mercedes coolers are left unpainted from factory im pretty sure(vito ones definatly are)
and i think the XR6 turbos may also be unpainted

id only worry about painting the cooler black if i was trying to hide it