A cooling device for a vehicle, having an inner housing with an inner cooling wall, and an outer housing which surrounds the inner housing, is spaced apart via a cooling gap and has an outer cooling wall. A cooling volume for passage of a cooling fluid is formed between the inner cooling wall and the outer cooling wall. The inner cooling wall and/or the outer cooling wall furthermore have channel walls for dividing the cooling volume and guiding the cooling fluid. At least one clamping device is arranged around the circumference of a circumferential wall of the outer housing for introducing a deformation force into the outer housing in order to reduce the cooling gap by deforming the outer housing.