A battery module (10) for the purely electric driving of a motor vehicle has a trough-shaped battery box (12) that runs around a circumferential direction, an inlet for feeding a coolant into a cooling space (30) partially bounded by the battery box (12), an outlet for conducting the coolant away from the cooling space (30), battery cells (14) in the battery box (12) and arranged in the cooling space (30), and an insulating layer (16) for fluid-tight sealing of the cooling space (30). At least one electrical pole (18) of the battery cell (14) projects out of the cooling space (30) through the insulating layer (16). The insulating layer (16) is formed from a previously liquid cured sealing compound. The insulating layer (16) can simultaneously make available a high sealing effect and a statically stabilizing effect for the battery box (12) together with a low intrinsic weight.