Generalizing the results of Faigle and Schrader [Inform. Process. Lett., 27 (1988), pp. 189–194] a short inductive proof is given that shows that the stationary distributions of a simulated annealing algorithm converge to a distribution, where nonoptimal elements are generated with probability zero, provided that the “weak reversibility condition” of Hajek [Math. Oper. Res., 13 (1988), pp. 311–329] holds.