An electric machine including a rotor shaft having an inner shaft core with a first composition and an outer shaft portion surrounding at least some of the inner shaft core. The outer shaft portion is fabricated from a material having a different composition than the inner shaft core. For example, the inner shaft core could be fabricated from a material having high thermal conductivity, such as copper, while the outer shaft portion is fabricated from a material with lesser thermal conductivity, but greater strength, for example steel. The two-material shaft with a highly thermally conductive core serves to conduct heat from the interior of the electric machine to the housing, or to an exterior apparatus or structure.