A sealing device for sealing the intermediate space between a housing and a shaft rotatably mounted in the housing, having a first plate-shaped body with a front face, a rear face, and a first opening, which extends from the front face to the rear face and is suitable for feeding through the shaft, and having a cooling line, which runs in the body and is suitable for conducting a cooling medium. The first body is suitable for being tightly secured to the housing such that the shaft rotatably mounted in the housing is guided through the first opening. The first opening is suitable for introducing sealant such that the sealant seals an intermediate space between the shaft and the first body. The cooling line is guided around the first opening between a cooling line inlet and a cooling line outlet for the cooling medium such that heat produced from rotating the shaft can be dissipated by the cooling medium in a spatially homogenous manner.