Battery module for a high-voltage battery of a motor vehicle, high-voltage battery and motor vehicle

A battery module for a high-voltage battery of a motor vehicle includes a cell stack with a plurality of prismatic battery cells stacked along a stacking direction, two end pressure plates, which are arranged on ends of the cell stack that are opposite one another in the stacking direction, and a cooling plate with a coolant connection for feeding and/or discharging a coolant. The coolant connection is formed so as to project in a vertical direction oriented perpendicularly to the stacking direction. At least one intermediate pressure plate, which is arranged between two battery cells within the cell stack and which has at least one passage opening along the vertical direction, in which passage opening the coolant connection is arranged and is led in the direction of a top side of the cell stack fluidically couples with at least one coolant line of the high-voltage battery.