First generation of highly conductive graphite composites with high thermal storage capacity of the (Na/K)NO3 eutectics salts opened next problems for improvement. Thermal stability limitations of newly produced composites require further fundamental research and development. The leakage of the salt from a graphite matrix, double peaks on a DSC curve, melting enthalpy differences between composites produced with melted salt eutectics (infiltration method) and those produced with mechanical mixtures of the salt components (cold compressed method), focused our examination on the salt eutectics, solidified in a graphite composite. Segregation problems of molten salt eutectics during melting in the composite structure; contribution of a larger interfacial contact in the solid solution of salt/graphite composite (compared to the crystallites of the single pure component salts) decided research on the control of salt eutectics crystallization process to achieve good thermal stability as a precondition for a high thermal capacity of the composite heat storage material.