This paper presents the modeling theory and results of an innovative thermal energy storage (TES) facility, ideated, realized, and tested by ENEA (Italy). This prototype enabled the thermocline storage with molten salts in a novel geometry ideated for small-medium scale decentralized solutions, which includes two vertical channels to force the circulation through two heat exchangers, respectively, and realized for charging and discharging phases (in a single tank). A thermophysical model was built and tested properly for this particular geometry in order to analyze the temperature distribution along the radius. The numerical results well reproduced the experimental values. Furthermore, the analytical solution provided a short-cut methodology able to evaluate the thermocline distribution (along the vertical axis) depending on both the time and the radius values. Hence, the influence of the radial position (r) on the thermocline degradation was studied finding that, at the edges (r → 1), the thermocline remains unchanged for longer (around ten times more) than at the center of the tank (r → 0). The obtained numerical modeling and the analytical correlation can be useful for the process analysis to scale-up the thermal storage system and to evaluate the system reliability for industrial plants.