This paper presents and demonstrates, by numerical simulation, a mixed-integer linear programming (MILP)-based Model Predictive Control (MPC) strategy for space-heating demand in buildings connected to a district heating system. The proposed MPC deals with space-heating demand with extended flexibility. It exploits thermal inertia, inherently present in the building and its heating system, to optimally plan space-heating load in anticipation of weather conditions and energy cost variations. MPC is based on a reliable Reduced-Order Model (ROM). Heating circuit and internal mass are carefully modelled within the ROM structure since these elements can be used for short-term heat storage and therefore play an important role in demand-side management. As for the model parameters identification, training data is restricted to non-intrusive, easily accessible measurements available at the substation level. The model identification approach and control strategy are applied to a well-insulated radiator-heated case-study building simulator developed in Modelica. Results show that the proposed ROM is reliable enough for an MPC application. Compared to conventional weather-compensation control, flexible MILP-based MPC proved to be cost-efficient, while preserving a decent indoor thermal comfort level.