A traction battery module for a vehicle, with a battery housing, the battery housing having a preferably extruded housing part with hollow chambers formed in it, which extend alongside one another along a central longitudinal direction and are open at the ends. The hollow chambers respectively define a cooling channel. At least one cooling connection adapter is provided, having a non-circular outer circumferential surface in an insertion portion and having been introduced or pressed at the end into one of the hollow chambers with an inner circumferential surface corresponding to the outer circumferential surface of the insertion portion. A pressing engagement is formed, at least in certain portions, between the outer circumferential surface and the inner circumferential surface.