In a system for feeding fluid into an exhaust gas after-treatment system, during operation fluid is fed via a feed line of the dispensing unit from a main container and is partially returned via a return line to the main container. A diaphragm pressure container is provided on the feed line downstream of a pump and a non-return valve toward the dispensing unit. During operation of the pump, the diaphragm pressure container is filled with fluid. The diaphragm pressure container is emptied as soon as the pump stops operating. In this way, the dispensing unit is cooled even after the operation of the system has ended, thereby protecting electronic components of the same from overheating.