We have calculated the thermal conductivity of pure KCl and KCl doped with RbCl using the Green-Kubo theory and classical molecular dynamics. Both shell-model and rigid-ion potentials are. employed to describe the ionic interactions, and we find that the inclusion of ionic polarisability significantly changes the calculated conductivity at a given temperature. We find fairly good agreement between the simulation results and the available experimental data for both pure and doped systems. The shell model provided a slightly better description than the rigid-ion potential, although neither proved to be entirely satisfactory over the temperature range investigated (300-900 K). The relative merits of the potentials are discussed in the light of these results, as are the technical issues raised by the calculations. These studies demonstrate the capacity of the approach to yield quantitative predictions of the transport properties of ionic materials using shell-model potentials. This will be of use in treating systems for which rigid-ion models are inadequate.