||Ionic liquids have been suggested as new engineering fluids, specifically in the area of heat transfer, and as alternatives to current biphenyl and diphenyl oxide, alkylated aromatics and dimethyl polysiloxane oils, which degrade above 200 degrees C, posing some environmental problems. Addition of nanoparticles to produce stable dispersions/gels of ionic liquids has proved to increase the thermal conductivity of the base ionic liquid, potentially contributing to better efficiency of heat transfer fluids. It is the purpose of this paper to analyze the prediction and estimation of the thermal conductivity of ionic liquids and IoNanofluids as a function of temperature, using the molecular theory of Bridgman and estimation methods previously developed for the base fluid. In addition, we consider methods that emphasize the importance of the interfacial area IL-NM in modelling the thermal conductivity enhancement. Results obtained show that it is not currently possible to predict or estimate the thermal conductivity of ionic liquids with an uncertainty commensurate with the best experimental values. The models of Maxwell and Hamilton are not capable of estimating the thermal conductivity enhancement of IoNanofluids, and it is clear that the Murshed, Leong and Yang model is not practical, if no additional information, either using imaging techniques at nanoscale or molecular dynamics simulations, is available.