NOVELTY - The fuel cell system (20) comprises a fuel cell stack (22) having a unit fuel cell comprising a cathode (23a), an anode (23b) and a polymer electrolyte membrane interposed the cathode and anode, a device (29) for detecting lack of humidification in the fuel cell stack, a water supplying device for supplying moisture to the fuel cell stack when lack of humidification is detected by the detecting device, a device for heating the supplied moisture, and a device (28) for cooling the supplied moisture, where the fuel cell stack is humidified by repeating heating and cooling the supplied moisture.    USE - The fuel cell system is useful as power source for household use and electric cars or for mobile devices such as cell phones and laptop computers.    ADVANTAGE - The fuel cell system is capable of rapidly humidifying the fuel cell stack when lacking humidification, can be humidified even at high temperatures without conducting power generation, is simple, light-weight and cost-effective, and can be rapidly manufactured with excellent output characteristics and long life characteristics.    DETAILED DESCRIPTION - The fuel cell system (20) comprises a fuel cell stack (22) having a unit fuel cell comprising a cathode (23a), an anode (23b) and a polymer electrolyte membrane interposed the cathode and anode, a device (29) for detecting lack of humidification in the fuel cell stack, a water supplying device for supplying moisture to the fuel cell stack when lack of humidification is detected by the detecting device, a device for heating the supplied moisture, and a device (28) for cooling the supplied moisture, where the fuel cell stack is humidified by repeating heating and cooling the supplied moisture by the heating device and the cooling device respectively. In the case where hydrogen gas is supplied as fuel to the anode, the fuel cell system includes a device for heating the fuel cell stack. The fuel cell stack heating device functions as the heating device for the supplied moisture. In the case where an aqueous methanol solution is supplied as fuel to the anode, the fuel cell system includes a device for supplying the fuel to the anode and a fuel cell stack cooling device for cooling the unit fuel cell. The fuel supplying device functions as the water supplying device and the fuel cell stack cooling device functions as the cooling device for the supplied moisture. The detecting device comprises a measuring device for measuring the output power or the internal resistance of the fuel cell stack or the hibernation time of the fuel cell stack, and a device for determining whether or not there is lack of humidification in the fuel cell stack based on information obtained by the measuring device. The fuel cell system further comprises a temperature controlling device for adjusting the temperature of the supplied moisture near to the operating temperature of the fuel cell stack by heating using the heating device, and adjusting the temperature of the supplied moisture near to room temperature by cooling using the cooling device. An INDEPENDENT CLAIM is included for a method for producing a fuel cell stack.    DESCRIPTION OF DRAWING(S) - The figure shows a block diagram of a fuel cell system.    Fuel cell system (20)    Fuel cell stack (22)    Cathode (23a)    Anode (23b)    Cooling device (28)    Detecting device. (29)