A shaft assembly and method for reducing the heat leak into the cryogenic region of a superconducting electrical machine comprising a rotor shaft extension assembly capable of transmitting large amounts of torque with substantially increased thermal impedance. The shaft assembly contains a plurality of concentric structural cylinders composed of high strength, low thermal conductivity structural materials. The structural cylinders are connected in series by means of welded joints or strong interlocking “finger” connections, in such a way that the coldest cylinder is connected to the cryogenic machine. An optional intermediate heat sink that allows the shaft extension member to rotate freely within the confines of the heat sink further reduces the heat leak into the cryogenic environment. Splined adapter hubs are typically used to connect the cylinder assembly to the rotor of the superconducting machine and the external device.