The purpose of this paper is to investigate a steady-state method enabling the measurement of the thermal conductivity of an electric conducting wire. Instead of varying the pulsation of a periodic current as done in the 3ω method, the proposed method is based on steady-state measurements realized for different lengths of the same wire. The model developed takes into account an external heat transfer coefficient (conduction + radiation) often neglected in previous works. A sensitivity analysis shows the possibility of estimating simultaneously the wire thermal conductivity and the external heat transfer coefficient. The experimental results obtained with Chromel and Copper wires are in good agreement with references values (less than 5% deviation).