A control unit is provided for fuel supply regulation during a cold-running phase of an internal combustion engine, that includes, but is not limited to an input port for inputting a combustion signal about the presence of a rich or lean combustion of a fuel mixture in the internal combustion engine, a P-element for providing a P-manipulated variable, which sets a fuel reduction upon the presence of a rich combustion and sets a fuel increase upon the presence of a lean combustion, an I-element for providing an I-manipulated variable, which sets a fuel increase, and an output port for controlling a fuel supply, the P-manipulated variable and the I-manipulated variable substantially offsetting one another during the cold-running phase upon the presence of a rich combustion in the stationary state.