The invention relates to a temperature-control device (1) for a battery system, at least comprising a cuboid-shaped hollow body (2) having at least one connection device (3) for supplying and at least one connection device (4) for discharging a separately temperature-controlled fluid, a plurality of regularly arranged and identical openings (7) extending from a first body surface (5) to a second body surface (6), wherein a cylindrical battery cell (8) is accommodated by each opening (7), such that a fluid-tight fluid chamber is formed, characterised in that, with the connection of the cell head (11) and the cell base (12), the hollow body (2) extends over a height h from > 20 to