An energy storage module (10) including a plurality of energy storage assemblies (12) electrically connected to one another, the module including an external casing (40) in which are arranged the storage assemblies (12) and at least one heat exchanger (24). The energy storage assemblies (12) are arranged side by side on at least two distinct levels (N1, N2). The heat exchangers (24) are positioned between two adjacent levels. The exchangers (24) are fixed to the casing (40) of the module at least at a securing wall (28) that is distinct from the contact faces (26A, 26B). The securing walls and the casing are configured so that the module has a space between the corresponding securing walls (28; 44) of the exchanger and of the casing.