The stress distribution in a rotating solid shaft with temperature dependent yield stress subject to a temperature cycle is investigated. It is presumed that the shaft is in a state of generalized plane strain and obeys Tresca's yield criterion and the flow rule associated with it. Even in an initially purely elastic shaft two plastic regions with different forms of the yield condition may emerge simultaneously at the centre. However, the expansion of the plastic zone ceases soon thereafter, and an unloaded region spreads into the plastic core; the latter process is treated in an approximate way. It is shown that the stress distribution is altered significantly by the temperature cycle, hence also leading to non-zero residual stresses at stand-still.