A gyroscopic roll stabilizer for a boat, the gyroscopic stabilizer comprising: an enclosure mounted to a gimbal for rotation about a gimbal axis and configured to maintain a below-ambient pressure; a flywheel assembly including a flywheel and flywheel shaft, with an open-ended cavity formed in an end of the flywheel shaft; a first bearing for rotatably mounting the flywheel assembly inside the enclosure for rotation about a flywheel axis; the first bearing comprising an inner race affixed to the flywheel shaft proximate the cavity and an outer race rotationally fixed relative to the enclosure; a motor operative to rotate the flywheel assembly; wherein: a liquid heat transfer medium is disposed in the cavity; a bearing cooling circuit (100") is configured to transfer heat away from the inner race of the first bearing by recirculating a cooling fluid, the bearing cooling circuit comprising: a heat transfer shaft assembly rotationally fixed relative to the flywheel axis and extending from the enclosure into the cavity so as to contact the liquid heat transfer medium; a closed fluid pathway for the cooling fluid that extends through the heat transfer shaft assembly to internally cool the heat transfer shaft assembly; the closed fluid pathway configured so that the cooling fluid remains separated from the heat transfer medium; wherein the gyroscopic roll stabilizer is configured to transfer heat away from the inner race of the first bearing to the flywheel shaft, and from the flywheel shaft to the liquid heat transfer medium, and from the liquid heat transfer medium to the heat transfer shaft assembly, and from the heat transfer shaft assembly to the cooling fluid. an enclosure mounted to a gimbal for rotation about a gimbal axis and configured to maintain a below-ambient pressure; a flywheel assembly including a flywheel and flywheel shaft, with an open-ended cavity formed in an end of the flywheel shaft; a first bearing for rotatably mounting the flywheel assembly inside the enclosure for rotation about a flywheel axis; the first bearing comprising an inner race affixed to the flywheel shaft proximate the cavity and an outer race rotationally fixed relative to the enclosure; a motor operative to rotate the flywheel assembly; wherein: a liquid heat transfer medium is disposed in the cavity; a bearing cooling circuit (100") is configured to transfer heat away from the inner race of the first bearing by recirculating a cooling fluid, the bearing cooling circuit comprising: a heat transfer shaft assembly rotationally fixed relative to the flywheel axis and extending from the enclosure into the cavity so as to contact the liquid heat transfer medium; a closed fluid pathway for the cooling fluid that extends through the heat transfer shaft assembly to internally cool the heat transfer shaft assembly; the closed fluid pathway configured so that the cooling fluid remains separated from the heat transfer medium; wherein the gyroscopic roll stabilizer is configured to transfer heat away from the inner race of the first bearing to the flywheel shaft, and from the flywheel shaft to the liquid heat transfer medium, and from the liquid heat transfer medium to the heat transfer shaft assembly, and from the heat transfer shaft assembly to the cooling fluid. a liquid heat transfer medium is disposed in the cavity; a bearing cooling circuit (100") is configured to transfer heat away from the inner race of the first bearing by recirculating a cooling fluid, the bearing cooling circuit comprising: a heat transfer shaft assembly rotationally fixed relative to the flywheel axis and extending from the enclosure into the cavity so as to contact the liquid heat transfer medium; a closed fluid pathway for the cooling fluid that extends through the heat transfer shaft assembly to internally cool the heat transfer shaft assembly; the closed fluid pathway configured so that the cooling fluid remains separated from the heat transfer medium; wherein the gyroscopic roll stabilizer is configured to transfer heat away from the inner race of the first bearing to the flywheel shaft, and from the flywheel shaft to the liquid heat transfer medium, and from the liquid heat transfer medium to the heat transfer shaft assembly, and from the heat transfer shaft assembly to the cooling fluid. a heat transfer shaft assembly rotationally fixed relative to the flywheel axis and extending from the enclosure into the cavity so as to contact the liquid heat transfer medium; a closed fluid pathway for the cooling fluid that extends through the heat transfer shaft assembly to internally cool the heat transfer shaft assembly; the closed fluid pathway configured so that the cooling fluid remains separated from the heat transfer medium; wherein the gyroscopic roll stabilizer is configured to transfer heat away from the inner race of the first bearing to the flywheel shaft, and from the flywheel shaft to the liquid heat transfer medium, and from the liquid heat transfer medium to the heat transfer shaft assembly, and from the heat transfer shaft assembly to the cooling fluid.