Optimal control theory has been used in the aerospace industry for many years. It has been applied to a wide variety of problems ranging from orbit transfer routes to missile tracking strategies. This paper discusses the application of optimal control theory to several residential heating and cooling systems. The optimal control strategy is determined and then approximations to that optimal strategy are presented. These approximate strategies are much easier to implement than the true optimal strategies. The performance of the approximate strategies relative to the optimal strategies is presented and shown to be an effective means for reducing utility peak demand.