The thermal conductivity of molten sodium chloride and potassium chloride has been computed through equilibrium molecular dynamics Green-Kubo simulations in the microcanonical ensemble (N, V, E). In order to access the temperature dependence of the thermal conductivity coefficient of these materials, the simulations were performed at five different state points. The form of the microscopic energy flux for ionic systems whose Coulombic interactions are calculated through the Ewald method is discussed in detail and an efficient formula is used by analogy with the methods used to evaluate the stress tensor in Coulombic systems. The results show that the Born-Mayer-Huggins-Tosi-Fumi potential predicts a weak negative temperature dependence for the thermal conductivity of NaCl and KCl. The simulation results are in agreement with part of the experimental data. available in the literature with simulation values generally overpredicting the thermal conductivity by 10%-20%. (C) 2004 American Institute of Physics.