A hydraulic fan drive for a cooling system of an internal combustion engine, in particular a diesel engine of a mobile working machine or a construction machine, is configured to be switched off for a short time or by way of a transition in dependence on a load of the internal combustion engine. A shut-off valve, which is arranged in a working line connecting a variable-displacement pump to a fan motor, is configured to switch off the fan drive. The fan drive is further configured to be switched off by rotational speed monitoring of the internal combustion engine.