A cooling support element for a stator segment of an electrical machine is provided. The cooling support element has a first and a second plate each having an upper surface and a lower surface. The upper surface of the first plate has anchoring element for anchoring a stator lamination stack attached to the cooling support element. The lower surface of the second plate has an inlet and an outlet opening. The two plates are attached to each other. The lower surface of the first plate faces the upper surface of the second plate. Separator elements are disposed between the lower surface of the first plate and the upper surface of the second plate for providing a cooling channel. A cooling fluid is guidable from the inlet opening through the cooling channel to the outlet opening for dissipating heat from the stator lamination stack.