An electric motor-driven water craft including a fuselage, on which a user can at least partially lie or stand. The fuselage has a flow channel with a screw that is driven by an electric motor and contains the electric motor and batteries, in addition to a control device for the electric motor and the screw, and those items are housed at least partially in the flow channel. This invention provides a higher power for motor-driven water craft of this type by locating the batteries in a water-tight housing. At least some sections of the batteries are in thermally conductive contact with the housing. The housing can be at least partially of a thermally conductive material and/or the electric motor is an internal-rotor motor. The stator is in thermal conductive contact with a housing of the electric motor by a heat conducting unit. At least part of the region of the housing that is assigned to the heat conducting unit can be of a thermally conductive material and the housing can be located at least partially in the flow channel.