NOVELTY - The apparatus (10) has a temperature detecting element such as thermistor (5) positioned in an electric-power generation cell (1) in a center of a cell stack (10S). A control circuit (6) stops the operation of the fuel cell stack, when the detected temperature is higher than a predetermined limit temperature.    USE - For use as power supply device for portable electronic devices such as mobile phone, notebook computer, etc.    ADVANTAGE - The heat generation of the electric-power generation cell can be detected rapidly before causing damage to the cell. The electric-power generation cell can be protected reliably. The cost of the apparatus can be reduced. The damage and deterioration to the fuel cell can de avoided by detecting the lack of fuel or the oxidizing agent.    DETAILED DESCRIPTION - The control circuit calculates a temperature-increase-rate of a selected electric-power generation cell from an output of the thermistor. The operation of the cell stack is stopped, when the temperature is lower than the predetermined limit temperature and the temperature increase rate is higher than the predetermined limit temperature increase rate. The limit temperature increase rate is defined according to the current output value of the cell stack. A normal operation is carried out to the other electric-power generation cell when a fuel supply or oxidizing agent supply becomes difficult to a selected cell. The selected cell carries out the normal operation when the temperature of an electric-power generation cell is higher than other cells. The selected cell is multiply arranged on both sides of the cell stack. The control circuit controls the output current of the cell. The circuit controls a fuel supply reduction unit for forcedly decreasing the fuel supply with respect to the cell. The circuit stops the operation of the cell, when the climbing speed of the detected temperature or temperature-rise velocity of the cell is higher than the predetermined limit temperature.    DESCRIPTION OF DRAWING(S) - The figure shows the structure of the fuel-cell stack. (Drawing includes non-English language text)    Electric-power generation cell (1)    Thermistor (5)    Control circuit (6)    Fuel-cell apparatus (10)    Cell stack (10S)