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. The work is partially funded by the Spanish Government (ENE2011-22722 and ULLE10-4E-1305). The authors would like to thank the Catalan Government for the quality accreditation given to their research group GREA (2014 SGR 123). The research leading to these results has received funding from the European Union׳s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. PIRSES-GA-2013-610692 (INNOSTORAGE). Laia Miró would like to thank the Spanish Government for her research fellowship (BES-2012-051861).