A metering device for introducing an operating medium into an exhaust manifold of an internal combustion engine, the device comprising a cooling system for cooling an injector module of the metering device. The cooling system is provided with a cooling circuit encompassing at least one cooling fluid and at least one cooling device which dissipates heat from the cooling circuit. A first portion of the cooling circuit is disposed at least in part below the cooling device and/or a second portion of the cooling circuit is located at least in part above a point that heats the cooling circuit, especially above the injector module.