Utility companies seek to increase energy efficiency and productivity and try to reduce peak loads. This often involves consumer-side demand management in residential areas using dynamic Time-of-Use (ToU) tariff. Such strategies work if the consumer-side response is at least partly automated using some real-time optimization strategy. Our paper proposes a consumer-side optimization and control framework for scheduling the electric appliances in a smart household and preserving a thermal comfort level through an electric heating system. Our framework consists of two optimization components interacting with each other. The first optimization component schedules the home appliances based on a Mixed Integer Programming approach. An electric vehicle (EV) is considered as a special home appliance with an energy storage capability. The second optimization component is the Model Predictive Control (MPC) strategy for the electric heating system, such that the input constraints are defined by the scheduling results of the first component. Due to outside temperature variations, the input constraints may impede the MPC to maintain the required thermal comfort, which triggers a rescheduling event for the first component. The efficiency of the framework is presented in multiple simulations for scenarios with different consumer behaviors.