A shaft seal of the rotating wheel shaft of a turbomachine includes a rotating wheel-side seal and a bearing-side seal between the bearing housing and the shaft. An oil outlet chamber is arranged between the rotating wheel-side seal and the bearing-side seal. The oil outlet chamber is delimited by a third seal between the bearing housing and the shaft, and a gas discharge chamber is arranged between the third seal and the rotating wheel-side seal. The construction is actively cooled by means of at least one splash oil bore in the region of the oil drain channel, as a result of which coking of the shaft seal can be prevented. The third seal separates the oil issuing from the oil outlet chamber from the gas issuing from the gas discharge chamber.