A cooling arrangement for an offshore wind energy installation, having a heat-absorbing device for absorbing heat generated by the electronic devices and/or the mechanical devices of the offshore energy installation, which is to be removed, and a coupled heat-dissipating device for dissipating heat to the surrounding water. The heat-absorbing device has a first cooling circuit operated by a fluid coolant which, in a heat exchanger device, transfers the absorbed heat to the heat-dissipating device having an open second cooling circuit operated with the ambient water as the coolant. A plurality of electrodes are arranged on the inner walls of the conduits of the second cooling circuit, which are spaced apart from each other in its extension direction, each of which is connected with a voltage supply device for generating an alternating high voltage between at least two of the electrodes.