NOVELTY - The system has a fluid channel (110) for conducting a cooling fluid to an electric machine (120) e.g. electric motor, of a motor vehicle (100). A receiving device (116) is arranged in the channel, and designed such that a part of an electrical energy storage system (118) is received and cooled by cooling fluid i.e. air, which flows through the channel. A ventilation device (122) i.e. impeller, is arranged in the channel, and initially conducts the cooling fluid to the receiving device for cooling the storage system and to the machine for cooling the machine.    USE - Cooling system for cooling an electrical energy storage system and an electric machine e.g. electric motor and generator, of a motor vehicle e.g. hybrid vehicle and electric vehicle (all claimed), where the motor is used for supporting an internal combustion engine and for producing propulsion, and the generator is used for producing electrical energy from brake energy.    ADVANTAGE - The receiving device is arranged in the fluid channel, and designed such that the part of the electrical energy storage system is received and cooled by the cooling fluid, which flows through the channel, thus avoiding the need for an additional blower for supplying cool air, and reducing apparative expenditure of the cooling system, and hence cost-effectively and efficiently cooling the storage system using a reduced number of parts, and achieving a high cooling efficiency of the system. The system requires a reduced installation space in the motor vehicle, ensures a perfect operation of the electric machine. The system has a simple structure and a high service life. The system ensures an optimal operating strategy based on heat dissipation.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for the following:    (1) a motor vehicle    (2) a method for cooling parts of an electrical energy storage system of a motor vehicle.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic block diagram of a cooling system for cooling an electrical energy storage system and an electric machine of a motor vehicle by common cooling fluid.'(Drawing includes non-English language text)'    Motor vehicle (100)    Fluid channel (110)    Receiving device (116)    Electrical energy storage system (118)    Electric machine (120)    Ventilation device (122)