Smart Grid has emerged a very important concept in modern power systems. The integration of different loads such as residential, commercial and industrial into the smart grid and their optimal operation has a significant effect on the system's reliability, stability, peak power demand and energy price. This work presents the mathematical modeling of a Centralized Temperature Control System (CTCS) of a Multi-Unit Residential Building (MURB) and its optimal operation considering electricity prices and weather variations. The model considers comfort levels, preference settings and activity of residents in different units of the building to determine the optimal operation schedules of the CTCS, minimizing its total energy consumption cost. Multi-objective operation of the MURB is also investigated when residents in different units have conflicting interests, and the impact of such conflicting preferences on the operation of CTCS is analyzed. A case-study on optimal energy management of a single unit house considering net-metering is also presented. The proposed CTCS model is a Mixed Integer Non Linear Programing (MINLP) model, where some of the constraints are linearized to reduce the computational complexity arising from the non-linearity, for real-time applications. The model is studied for various customers' preferences using a realistic MURB model. Simulation results show that significant cost savings can be achieved using the proposed mathematical model.