In order to design the current carrying conductor for GIS, it is important to predict temperature-rise when rated current flows in the bus bar. However, it is not easy to apply the correct heat transfer coefficient on the boundary between different material for the thermal analysis. In this paper, the heat transfer coefficient which depends on parameters such like material constant, model geometry as well as ambient temperature, was calculated by analytic method. The calculated coefficient is used for the temperature rise prediction by F.E.M. The results show good agreement with experimental data.