Battery module having: a plurality of battery cells, each comprising at least one first electrode and at least one second electrode, and a separator are positioned between the first electrode and the second electrode, and a battery cell housing, which comprises a first housing half and a second housing half, wherein the first housing half is electrically insulated from the second housing half and wherein the first electrode is electrically contact-connected to the first housing half and the second electrode is electrically contact-connected to the second housing half, wherein the first electrode and the second electrode are aligned in parallel with a bottom face or a top face of the battery cell, and wherein the bottom face and the top face of the battery cell housing are embodied in the form of a regular hexagon, and a battery module housing, which has side walls and a top face and a bottom face, wherein the battery cells are contact-connected both in the region of the bottom face and in the region of the top face of the battery module housing, wherein the battery cells are arranged spaced apart from one another in a horizontal plane so that a throughflow option in the form of temperature-control medium channels for a temperature-control medium is produced between the side faces of adjacent battery cells, as a result of which the temperature-control medium can flow along the side faces of the battery cells, wherein the battery module housing has a temperature-control medium inlet and a temperature-control medium outlet and wherein the temperature-control medium can flow through the battery module housing in the horizontal plane. a plurality of battery cells, each comprising at least one first electrode and at least one second electrode, and a separator are positioned between the first electrode and the second electrode, and a battery cell housing, which comprises a first housing half and a second housing half, wherein the first housing half is electrically insulated from the second housing half and wherein the first electrode is electrically contact-connected to the first housing half and the second electrode is electrically contact-connected to the second housing half, wherein the first electrode and the second electrode are aligned in parallel with a bottom face or a top face of the battery cell, and wherein the bottom face and the top face of the battery cell housing are embodied in the form of a regular hexagon, and a battery module housing, which has side walls and a top face and a bottom face, wherein the battery cells are contact-connected both in the region of the bottom face and in the region of the top face of the battery module housing, wherein the battery cells are arranged spaced apart from one another in a horizontal plane so that a throughflow option in the form of temperature-control medium channels for a temperature-control medium is produced between the side faces of adjacent battery cells, as a result of which the temperature-control medium can flow along the side faces of the battery cells, wherein the battery module housing has a temperature-control medium inlet and a temperature-control medium outlet and wherein the temperature-control medium can flow through the battery module housing in the horizontal plane.