The temperature profile along a cylindrical rod or tube as it cools has been obtained by numerical solution of the second-order time-dependent partial differential equation for heat conduction. The surface temperature is calculated for given temperature dependent values of the heat capacity, hemispherical total emissivity, thermal expansion and thermal conductivity and, by adjusting the thermal conductivity, is fitted to experimental temperature profiles obtained from preliminary measurements on a cooling cylindrical tungsten rod. The surface temperature of the rod is quite sensitive to the thermal conductivity but the accuracy of the predicted thermal conductivity cannot be assessed without further experimentation.