The invention relates to a temperature-control device (1) for a battery system, at least comprising a cuboid-shaped hollow body (2) with 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 identically formed 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), so that a fluid-tight liquid space is formed, which is characterized in that the hollow body (2), excluding the cell head (11) and the cell bottom (12), extends over a height h of >20 to