This work presents a numerical investigation of the thermal control performance of a phase change material (PCM) composite-filling fin heat exchanger under natural convection and transient heat flux shocks. First, the temperature control performance of the PCM-based fin heat exchanger and the fin heat exchanger without PCM is compared. Then, the influence of the PCM filling patterns, liquid phase change temperature, and the PCM filling volume fraction on the temperature control performance are studied. The results show that filling the PCM in fins could significantly improve the temperature control performance by absorbing heat during the solid–liquid phase change process. Compared with the fin heat exchangers without PCM, the temperature control performance of the designed PCM-based fin heat exchangers could be improved by up to 13%. PCM filling patterns influence the temperature control performance of fin heat exchangers to a certain extent, and the asymmetric filling pattern is better than the symmetric filling pattern. The results of different phase change temperatures of PCM show that, within a certain temperature range, the lower the liquid phase change temperature results in a better temperature control performance since more PCM would melt when suffering the heat flux shock. Besides, when the volume fraction of PCM is small, it also greatly influences the temperature control efficiency of the heat exchanger; however, when the volume fraction of PCM is larger than 75%, its influence could be neglected.