The thermal conductivity data for molten NaNO3 and KNO3 have been examined in order to propose recommended data sets for these two popular heat carriers and to establish the reference values above the temperature range covered by toluene and water. It is known that the measurement of the thermal conductivity of molten salts is very difficult, owing mainly to their corrosiveness and high melting temperatures, which introduce complications in apparatus design and significant systematic errors due to radiation and convection. However, some recent measurements seem to manifest more trustworthy values than obtained before. All available data have been collected and critically evaluated. The temperature range covered is 584 to 662 K for molten NaNO3 and 662 to 712 K for molten KNO3, with the confidence limits better than ± 5%.