Battery module of a high-voltage battery for an electric vehicle

A battery module for an electric vehicle has battery cells stacked behind one another to form a battery cell package in a multipart battery module housing. An end plate is on an end of the battery cell package. The battery module housing has a central portion and a housing end plate at an end of the central portion. A gap between the battery cell package and an inner surface of the central portion is filled with a thermally conductive medium. The end plate has a spraying point for introducing the thermally conductive medium and a distribution channel for guiding the thermally conductive medium from the spraying point into spaces between the battery cell package and the inner surface of the central portion.