The emissivity of copper is not from 0.7 to 0.88 unless its surface has been oxidized or significantly modified in some other way. For electrical work, 0.4 does not seem to be a good guess for copper emissivity. Even if you google "copper emissivity", the first hit you get is of a company...
What ericgrau posted is accurate. Of the three heat transfer modes from the bare wire, natural convection dominates over conduction and radiation. Any introductory heat transfer book (Incropera and DeWitt, Fundamentals of Heat and Mass Transfer) discusses these heat transfer modes, and their...