In fuel-cell-powered vehicles, the fuel-cell system requires a thermal-management subsystem to dissipate heat released during the reaction of hydrogen with oxygen. When the stack generates power at a high rate, a large amount of heat is also generated. If cooling by the radiator is insufficient, a supplementary stack-cooling system is needed to maintain a safe operating temperature. In this study, the performance of a $CO_2$air-conditioning unit for stack cooling was investigated under various conditions, and the relationship between cabin cooling and stack cooling was also studied. The coefficient of performance (COP) increased from 1.9 to 2.4, with an increase in cabin-air inlet flow rate from 0 to 8 $m^3$/min. When the airconditioning unit was turned off, the cooling capacity of the stack cooler was increased; correspondingly, as the cabin-cooling capacity was increased, that of the stack cooler decreased. With an increase in ambient-air inlet temperature from $38^{circ}C$ to $45^{circ}C$, the COP decreased by 24%. Additionally, both the stack-cooling capacity and cabin-cooling capacity were decreased by about 12% and 16%, respectively, due to reduced heat transfer in the gas cooler as the ambient air inlet temperature was increased. It is expected that the experimental results can serve as a resource in designing a stack-cooling system using a $CO_2$air-conditioning unit to enhance stack power generation and efficiency.