The invention relates to a housing (10) for accommodating a plurality of battery cells (20), in particular lithium-ion battery cells, wherein the housing (10), in particular a plastic housing, comprises a cooling device with an inlet point (30) and an outlet point (40) for an air stream (22) for cooling the battery cells (20). In addition, the housing (10) is designed as a single piece together with the cooling device integrated in the housing (10), and the cooling device additionally has spacers (34; 34a, 34b) for arranging all accommodated battery cells (20) with an intermediate space (23) for guiding air between the battery cells (20), by which means an air channel (25) is provided for the air stream (22) between the battery cells (20). The invention further relates to a battery pack (50) and to a motor vehicle comprising such a battery pack (50).