The fuel cell system according to the invention serves to generate power and heat from liquid and gaseous fuels. It has a reformer and a fuel cell stack whose working temperature is above 120°C and whose waste heat is used to generate water vapour in vapourization ducts (2). The vapourization ducts (2) are arranged in direct thermal contact with the stack (1) to be cooled. By means of a pressure-maintaining device at the outlet of the vapourization ducts (2), the pressure in said vapourization ducts (2) is set to a value which produces the desired stack temperature.