A system for the water vapor reforming of a hydrocarbon includes an evaporator, a prereforming unit, a main reformer, a CO removal unit and at least one catalytic burner unit. A first burner unit is in a thermal contact with the evaporator and a second burner unit is in a thermal contact with the main reformer, and the prereforming unit is in a thermal contact with the CO removal unit by way of one heat conducting separating medium. In addition, the outlet of the CO removal unit is connected with the inlet of the at least one burner unit. During a cold start, a heating-up operation is carried out during which first the two burner units are activated with an external feeding of hydrogen or hydrocarbon, and the reforming operation is started with a hydrocarbon fraction that is lower than in the normal operation. The resulting reformate gas, instead of the externally fed hydrogen or hydrocarbon, is introduced as fuel into the burner units.