NOVELTY - The device has latent heat accumulators formed as a heat storage (4), a control storage (5) and/or a cold storage (6). Switching elements are controllable such that the heat accumulators are functionally coupled or decoupled to coupling elements (1). The coupling elements, switching elements, heat accumulators and heat-conductive connections (2) are functionally connected with each other such that heat transmission between an electrochemical energy store (9) and heat accumulators is controllable and/or regulatable by the switching elements.    USE - Device for air-conditioning of an electrochemical energy store e.g. fuel cell such as alkaline fuel cell, proton exchange membrane fuel cell, direct-methanol fuel cell, phosphoric acid fuel cell and molten carbonate fuel cell, and battery such as lead battery, nickel cadmium battery, lithium ion battery, silicon battery and lithium polymer battery, in an air-conditioned electrical energy supply device of a motor vehicle (all claimed). Can also be used for electric vehicle and plug-in hybrid electric vehicle.    ADVANTAGE - The device is designed such that increased safety of the energy store is achieved by avoiding explosions, protection against supercooling of the energy store is achieved, functional availability of the energy store is increased at low temperatures, and increased temperature stability is achieved while achieving reduction of thermal aging effects of the energy store. The device enables efficiency improvement of the energy store, achieves reduction of fuel consumption and lower energy consumption for air conditioning and realizes reduced dimension of the energy store and/or reduction of system costs.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a method for air-conditioning of an electrochemical energy store.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of an air-conditioned electrical energy supply device with an electrochemical energy store.    Coupling elements (1)    Heat-conductive connections (2)    Heat storage (4)    Control storage (5)    Cold storage (6)    Electrochemical energy store (9)