In most typical situations, thermal energy storage (TES) systems, which incorporate sensible and latent storage capacities, are not effectively utilized within the overall functions of building energy management systems (BEMSs), which usually rely on classical rule-based control (RBC). This study addresses the challenge of overcoming this by featuring model predictive control (MPC). The proposed method is based on modeling a water tank-integrated phase change material (PCM) using data-driven linear approximation generated with sparse regression. Based on the control objective, the proposed MPC can address two control targets, either providing robust and fast-tracking to the TES charging/discharging setpoints or reducing the energy cost related to the building heating needs. The digital simulation of a two-day scenario, using real operation conditions, demonstrates the effectiveness of the proposed MPC framework, showing up to 57 % heating cost reduction compared to the RBC scenario. As the real-time control requirement is critical, the MPC computing time was evaluated to assess its potential for integration into real-world applications within BEMS.