A gyroscopic roll stabilizer comprises a gimbal having a support frame and enclosure configured to maintain a below-ambient pressure, a flywheel assembly including a flywheel and flywheel shaft, one or more bearings for rotatably mounting the flywheel inside the enclosure, a motor for rotating the flywheel, and bearing cooling system for cooling the bearings supporting the flywheel. The bearing cooling system enables heat generated by the bearings to be transferred through the flywheel shaft to a heat sink disposed within a cavity in the end of the flywheel shaft, or to a liquid coolant circulating within the cavity.