This work presents the implementation of a Model Predictive Control (MPC) scheme used to study the improvement of the thermal quality in aged residential buildings without any rehabilitation. The controller manages the heating system of an experimentally characterized model of a residential dwelling in a social block built during the decade of the 1960s located in the neighborhood of Otxarkoaga (Bilbao, Spain), so as to obtain an optimal energy efficiency performance. Due to the characteristics of the construction in those days, this kind of buildings suffer problems related to the use of awkward building materials and inefficient heating systems. A comparison with traditionally used ON-OFF hysteresis control is presented in order to demonstrate the energetic improvement provided by the MPC scheme. Besides, the variation of different parameters of the MPC is also studied to determine its influence over the energy consumption and comfort conditions.