In the design of thermal protection system for hypersonic vehicles, the efficient convective heat transfer within regenerative cooling channels plays a critical role in maintaining their thermal performance. This study focuses on the topology optimization (TO) of the cooling channels that operate at high Reynolds number and have variable thermo-physical properties. A novel approach is introduced to enhance the density-based method by incorporating an effective artificial force correction and tabulating the temperature-dependent thermal properties. Several topology-optimized cooling layouts were generated to minimize the maximum temperature within the design domain while considering different power dissipation constraints. This confirms the validity of the proposed lumped correction term in momentum equation accounting both viscous and convective body forces. Regarding the thermal performance of the optimized layouts, the staggered arrangement of cellular ribs in the TO channel was found to induce multiple flow separations and promote turbulent mixing, thereby improving heat transfer efficiency and mitigating the thermal acceleration effect. Conjugate heat transfer calculations revealed that the optimal topology-optimized channel achieved a 24.3% improvement in overall thermal performance while being 15.3% lighter than the straight channel design. Furthermore, the optimal topology optimized layout consistently outperformed the straight channel design by 6.6% to 24.3% in terms of the overall thermal performance across a wide range of heat flux distribution and mass flow rate conditions. This investigation highlights the effectiveness of topology optimization in designing regenerative cooling structures featuring high Reynolds number hydrocarbon thermal fluid flow.