The utilization of a lithium-cooled nuclear power supply system in conjunction with the He-Xe Brayton power system has great potential for providing power for space exploration missions. This is primarily attributed to its notable characteristics, such as high energy density, substantial output power, long-duration operation cycle, and little vulnerability to environmental factors. One of the salient concerns that necessitates attention is the phenomenon of heat transfer occurring between liquid lithium and a mixture of helium and xenon (He-Xe). The Vertical Cross-Flow Corrugated Plate Heat Exchanger (VC-CPHE) constructed from W-alloy possesses several advantages in space reactor applications compared to other heat exchangers. These include its compact design, which allows for a large heat exchange surface, as well as its ability to shield gamma-ray radiation. This paper investigates the thermal hydraulic properties of the VC-CPHE internal heat transfer medium using Computational Fluid Dynamics (CFD) techniques. The results indicate that, due to the similar flow channel structure of Li and He-Xe, there are similarities in terms of flow direction and periodic distribution of parameters. Nevertheless, due to the distinct thermophysical properties and operational parameters, these materials demonstrate notable disparities in temperature boundary layers, local thermal resistance, and other relevant factors. Furthermore, the optimization of VC-CPHE involves a balancing act between enhancing heat transfer efficacy and minimizing flow resistance. The VC-CPHE demonstrates optimal balanced performance when the inlet cross-angle is set at 45°. In comparison to Li, He-Xe exhibits elevated levels of thermal resistance and pressure loss. Hence, in the investigation of optimizing the corrugation pitch and inlet cross-angle, the optimal balanced size of corrugation pitch is 12 mm and inlet cross-angle is 45° on He-Xe side is used as the final result. An increase in the inlet temperature difference of the heat exchanger leads to a slight decrease in the heat transfer coefficient, but an overall improvement in heat transfer. On the basis of obtaining the flow and heat transfer characteristics inside VC-CPHE, the effects of inlet cross-angle, corrugation pitch, and inlet temperature difference on the performance of VC-CPHE are discussed. The findings derived from the present study provide valuable insights for the future design and optimization of VC-CPHE systems in megawatt-class nuclear power deep space exploration spacecraft, particularly in relation to internal heat transfer.