This review is focused on the study of the requirement of high thermal conductivity of thermal energy storage (TES) materials and the techniques used to enhance it as this is one of the main obstacles to achieve full deployment of TES systems. Numerical and experimental studies involving different thermal conductivity enhancement techniques at high temperature (>150 °C) are reviewed and classified. This article complements Part 1, which reviews the different requirements that TES materials and systems should consider for being used for high temperature purposes and the approaches to satisfy them. The enhancements identified for this temperature range are the addition of extended surfaces like fins or heat pipes and the combination of highly conductive materials with TES material like graphite or metal foam composites and nanomaterials. Moreover the techniques presented are classified and discussed taking into account their research evolution in terms of maturity and publications.