Featuring phase-change energy storage, a mobile thermal energy supply system (M-TES) demonstrates remarkable waste heat transfer capabilities across various spatial scales and temporal durations, thereby effectively optimizing the localized energy distribution structure—a pivotal contribution to the attainment of objectives such as “carbon peak” and “carbon neutral”. To heighten the efficiency of energy transfer for mobile heating, this research introduces the innovative concept of modular storage and transportation. This concept is brought to life through the development of a meticulously designed modular mobile phase-change energy storage compartment system. Employing computational fluid dynamics (CFD), an in-depth exploration into the performance of the modular M-TES container and the adapted phase-change material (PCM) is conducted. By implementing fin arrangements on the inner wall of the heat storage module, a remarkable upsurge in the liquid phase-transition rate of the phase-change material is achieved in comparison to the design lacking fins—this improvement approximating around 30%. However, it is essential to acknowledge that the augmentation in heat transfer gradually recedes with the proliferation of fins or an escalation in their height. Moreover, the integration of expanded graphite into erythritol emerges as profoundly effective in amplifying the thermal conductivity of the PCM. Notably, with the addition of a 15.2% volume fraction of expanded graphite to erythritol, the duration of heat storage experiences a drastic reduction to nearly 10% of its original duration, thereby signifying a momentous advancement in thermal performance.