Hi Munna, welcome here!
You mean, heat transfer from copper to air? No worry with copper oxide or any tarnishing there. This transfer is limited by the properties of air; solids are so much better that their effect is negligible.
Just for comparison: air at room temperature conducts some 0.025W/m/K, pure copper 390W/m/K, most oxides 1 to 10W/m/K, so a thin oxide later is negligible. Transfers to air work because turbulence brings fresh air near to the solid. If air is immobilized, say by some foam, it becomes an excellent insulator, better than brick for instance.