A carburetor has a housing wherein a control drum is rotatably mounted. A section of an intake channel is formed in the carburetor. A subsection of this section is formed in the control drum. The control drum controls the free flow cross section of the intake channel. A fuel opening is connected to a fuel chamber via an unbranched fuel channel which opens into the subsection of the intake channel. A simple configuration of the carburetor is achieved by the carburetor including an electrically actuated valve which controls the flow of fuel through the fuel channel. For a method for operating an internal combustion engine with a carburetor, a temperature (T) is determined before or during the starting of the engine and that the flow of fuel through the fuel channel during the starting of the engine is controlled in dependence upon the temperature (T).