There is close relation between the heat generation in the fuel cell stack and the fuel performance. In PEM fuel cell vehicles, the stack coolant temperature is about $65^{circ}C$, which is far lower than that for general automobile engine. Therefore, it is hard to release heat generated in the stack by using a radiator of limited size because of the reduced temperature difference between the coolant and the ambient air. In this study, indirect stack cooling system using $CO_2$ heat pump was designed and its stack cooling performance in releasing heat to the ambient was investigated. This work focuses on a series of processes that grasp the relation among the fuel cell power, the radiator capacity and the stack temperature. The purpose of this work is to find out a way to properly release sufficient amount of heat through the finite sized radiator, so that the slack power generation can not be deteriorated due to the stack temperature increase. The optimization between the compressor power consumption and the fuel cell output power can be carried out to maximize the performance of fuel cell system.