Previous work by the author entailed modeling of the Packed Bed Thermal Energy Storage System, utilizing Phase-Change Materials, and a performance evaluation of the system based on the Second Law of thermodynamics. A principal conclusion reached is that the use of a single family of phase-change storage material may not in fact produce a thermodynamically superior system relative to one utilizing sensible heat storage material. This prompted us to modify our model so that we could investigate whether or not a significantly improved performance may be achieved via the use of multiple families of phase-change materials instead. Other factors investigated in the present work include the effect on system performance due to the thermal mass of the containment vessel wall, varying temperature and mass flow rate of the flue gas entering the packed bed during the storage process, and thermal radiation which could be a significant factor at high temperature levels. The resulting model is intended to serve as an integral part of a real-time simulation of the application of a high temperature regenerator in a periodic brick plant. This paper describes the more comprehensive model of the high temperature thermal energy storage system and presents results indicating that improved system performance could be achieved via a judicious choice of multiple families of phase-change materials.