A thermal contact and filling material having at least one thermally conductive filler and at least one silicone-free base oil. The thermally conductive filler is a metal hydroxide, in particular aluminum hydroxide, and the thermal contact and filling material also has at least one chemically crosslinkable prepolymer mixture. A storage battery assembly, in particular for a vehicle, is provided including at least one carrier, at least one storage battery element, which storage battery element is arranged on the carrier, and at least one bottom plate, wherein the carrier is arranged on the bottom plate. The storage battery assembly includes, at least between the bottom plate and the carrier and/or between the storage battery element and the carrier, a thermally conductive layer, which is formed of the thermal filling and contact material.