A heat exchanger for a battery unit having at least a first battery module and a second battery module is disclosed wherein the first and second battery modules each include a plurality of battery cell containers each housing at least one battery cell. The first and second battery modules are spaced apart from each other with the heat exchanger being arranged between the spaced apart first and second battery modules. The heat exchanger is a laminated plate structure defining a plurality of fluid flow chambers each located within a respective fluid flow region for transmitting a heat exchanger fluid. Each of the fluid flow regions is dimensionally compliant independent of the other fluid flow regions to conform to the spacing of the respective battery cell containers in the first and second modules between which the specific fluid flow region is positioned when arranged between the first and second battery modules.