A centrifugal separator includes a frame and a drive member configured to rotate a rotating part in relation to the frame around an axis of rotation. The rotating part includes a centrifuge rotor enclosing a separation space. The centrifuge rotor is adjoined to a hollow spindle supported by the frame by at least one bearing device. The interior of the hollow spindle is in thermal contact with the at least one bearing device and further includes a thermal transfer medium inlet for supplying a thermal transfer medium to said interior and a thermal transfer medium outlet for withdrawing the thermal transfer medium from the interior; and directing mechanism for directing thermal transfer medium from the thermal transfer medium inlet to the thermal transfer medium outlet in a first direction along the length of the spindle and in a second direction along the length of the spindle. The second direction is opposite the first direction. The first or second direction is along the inner wall of the interior of the spindle, the inner wall being arranged to rotate during operation of the centrifugal separator.