This paper describes the optimal control of operation of the auxiliary heating system used as backup in a passive-solar-heated system. A specific application is studied for a residence heated using a combined sunspace Trombe-Wall passive system solar system and an electrically heated thermal storage floor to satisfy the heating requirements of the house. The mathematical model of the general solution is derived and the optimal control determination using the maximum principle technique is described. The present work is a continuation of previous work done by Bakos [Energy Build. 31 (21000) 237].