A line supply arrangement for electrically powered motor vehicles includes an electric line on a support arm above the motor vehicle. A trolley on the support arm positions the electric line such that a free end thereof hangs down from the trolley for connection to the motor vehicle and charging of an energy store. The trolley is movable relative to the support arm in horizontal direction or the support arm is movable and the trolley relative to the support arm in horizontal direction. Arranged on the trolley is a line reel to lower the free end of the electric line to the motor vehicle, and a hose reel is fixed on the support arm for supply and discharge of cooling liquid to and from the electric line. The trolley is movable relative to the hose reel. A heat exchanger is arranged distal to the trolley for cooling the cooling liquid.