A turbine shaft may be used to remove a heat load from pliant bearings without requiring the use of a process fluid for cooling the turbine shaft. The turbine shaft comprises a heat conductive sleeve disposed between an outer surface of a tie rod shaft and an inner surface of a bearing journal; the heat conductive sleeve having a sleeve inner surface separated from a sleeve outer surface by a sleeve thickness; the heat conductive sleeve having a first end separated from a second end longitudinally about a center axis; the sleeve outer surface being in physical contact with the inner surface of the bearing journal; and the heat conductive sleeve having a thermal conductivity that is greater than a thermal conductivity of the bearing journal.