The invention relates to a cooling device with at least one first cooling duct element comprising at least one first cooling duct, and at least one second cooling duct element comprising at least one second cooling duct, where the first and the second cooling duct element each have a circular arc-shaped basic shape around a central axis of the cooling device. The first cooling duct element and the second cooling duct element are arranged concentrically to one another, where the second cooling duct element is arranged with respect to the first cooling duct element in such a way relative to the central axis that the first and the second cooling duct overlie each other along the first and the second cooling duct element at least in part in the radial direction. The invention further relates to a motor housing and a motor unit.