A battery module (10) has a first and second partial modules (12, 16) with first and second battery cells (14, 18) respectively. A cooling medium for cooling the first battery cells (14) is in a first volume that is bounded by a first partial housing (28) and can flow through the first partial module (12), and a cooling medium for cooling the second battery cells (18) in a second volume bounded by a second partial housing (34) can flow through the second partial module (16). The first partial housing (28) has a first tubular flange (36) projecting into a first intermediate space (24) between the first battery cells (14), and the second partial housing (34) has a second tubular flange (38) projecting into a second intermediate space (30) between the second battery cells (18). The first and second volumes are connected via the first and second tubular flanges (36, 38).