Proton exchange membrane hydrogen fuel cells (PEMFCs) are promising energy conversion devices, capable of directly converting chemical energy into electrical energy. However, the ideal operating temperature range for PEMFCs is narrow, and the intense exothermic reactions can easily lead to internal temperatures exceeding optimal levels. Thus, carefully designed cooling channels are crucial to maintain proper operating temperatures. Drawing inspiration from the heat dissipation characteristics of human capillaries on the skin, this study develops three biomimetic capillary cooling channels using a two-objective topology optimization approach. The heat transfer performance of these biomimetic cooling channels is compared against traditional parallel channels (TPC). Additionally, two new flow channel designs with varying inlet and outlet configurations are analyzed. The study examines the impact of different weight factors on the biomimetic cooling channels and uses Pareto frontiers to compare the results from varying weight factors. Findings indicate that topology-optimized biomimetic cooling channels can significantly enhance overall performance. Using a PEC = 1 for TPC as a benchmark, the biomimetic channels achieve average PECs of 1.72, 3.03, and 3.77, indicating superior performance over TPC. Furthermore, the ratio of weight factors also plays a role in the formation of cooling channels. The model with a weight factor ratio of w1:w2 = 0.6:0.4 for double inlets and double outlets arranged in opposite directions shows improved performance. Lastly, this study outlines a design guideline for PEMFC cooling channels based on biomimetic capillary structures and the appropriate ratio of the double objective functions to enhance heat dissipation performance.