Phase-change thermal storage technologies are becoming increasingly indispensable in the field of renewable energy, and researchers have been striving to achieve high thermal storage performance in storage devices. To enhance the application potential of phase-change thermal storage units based on micro heat pipe arrays, theoretical analysis is applied to optimize the operating parameters and the fin structure, addressing the research gap caused by insufficient theoretical analysis. Therefore, an accurate thermal resistance network model is developed, and machine learning algorithms are employed for the multi-objective optimization of the fin structure. The optimal heights, widths, and thicknesses in two directions of the fins are 42.2, 3.7, 0.3, and 0.8 mm, respectively, resulting in a 15.8 % increase in charging power compared to the initial structure without increasing metal consumption. Additionally, it is recommended that the design flow rate be increased by 26 kg/h for each additional thermal storage unit connected in series. Finally, a phase-change thermal storage device is designed for a solar water heating system, and its applicability is simulated and analyzed. This study provides design guidance for this novel thermal storage device and promotes its application in the field of renewable energy.