An electrical battery includes a plurality of electrical energy generating elements formed by at least one electrochemical cell that is packaged in a flexible sealed envelope, and a system for the mechanical and thermal conditioning of the elements. The conditioning system forms a structural body made from thermally conductive material. The body has two longitudinal members and a plurality of cross-members connecting the longitudinal members so as to form between the cross-members housings in which respectively a generating element is disposed. The body includes a circulation path for a thermal conditioning fluid. The path has two channels, respectively upstream and downstream, that are formed respectively in a longitudinal member and passages formed in each of the cross-members. The passages are in fluid communication on each side with respectively the upstream channel and the downstream channel.