The effects of T-shaped fins on the improvement of phase change materials (PCM) melting are numerically investigated in vertical triple-tube storage containment. The PCM is held in the middle pipe of a triple-pipe heat exchanger while the heat transfer fluid flows through the internal and external pipes. The dimension effects of the T-shaped fins on the melting process of the PCM are investigated to determine the optimum case. Results indicate that while using T-shaped fins improves the melting performance of the PCM, the improvement potential is mainly governed by the fin’s body rather than the head. Hence, the proposed T-shaped fin did not noticeably improve melting at the bottom of the PCM domain; additionally, a flat fin is added to the optimal case (Added-Fin case) and compared to the No-Fin, Uniform-Fin, and Optimum T-shaped Fin cases (no added fin). The analysis shows that the total heat storage rate of the Added-Fin case increased by 141.7%, 58.8%, and 47.6% compared with the No-Fin, Uniform-Fin, and the Optimum T-shaped Fin cases, respectively. Furthermore, the total melting time for the Added-Fin case was 1882 s and decreased by 59.6%, 38.4%, and 33.6% compared with those of the No-Fin, Uniform-Fin, and the Optimum T-shaped Fin (Optimum) cases, respectively.