The great development of energy storage technology and energy storage materials will make an important contribution to energy saving, reducing emissions and improving energy utilization efficiency. Mobile thermal energy storage (M-TES) technology finds a way to realize value for low-grade heat sources far beyond the demand side. In this paper, an indirect-contact M-TES container is studied using the computational fluid dynamics (CFD) method. By optimizing the heat exchange tube bundle layout and the installed fin structure of the shell and tube type M-TES container, a method of enhancing the charging and discharging efficiency is identified. The peripheral distribution mode of the heat exchanger tubes improves the efficiency of heat charging by 12.6% compared with the traditional uniform layout. The installation of the Y-shaped fins can improve the heat charging efficiency by 8.3%, better than straight fins. Compared with the horizontal installation of Y-shaped fins, the vertical installation of Y-shaped fins is preferred to improve the heat charging efficiency of the M-TES container.