Heating, ventilation and air-conditioning (HVAC) systems must hold the indoor temperature within prescribed limits, and doing so with less energy is a central problem in building energy management. This paper develops a two-layer hierarchical model predictive control (HMPC) scheme and evaluates it in simulation for a representative 100 m² administrative office zone in Az Zawiyah, Libya. The upper-layer MPC, with a 1-h sampling interval and an 8-h horizon, optimizes the indoor temperature reference by weighing reference tracking against HVAC power and setpoint smoothness. Beneath it, a lower-layer MPC with a 5-min sampling interval and a 1-h horizon regulates the zone temperature and is coordinated with the upper layer through a supervisory power target. Both layers share a control-oriented second-order resistance–capacitance (2R2C) thermal model; its zero-order-hold discretization reproduces a high-resolution continuous-time reference simulation with an RMSE of 0.107 °C and R² = 0.9998. We compare the HMPC with single-layer MPC and a conventional PID baseline in four 24-h scenarios: mild spring, winter heating, severe summer cooling and an autumn transition with variable internal gains. Both predictive controllers keep the indoor temperature inside the 20–24 °C band 100% of the time, whereas PID averages 76.30%. Single-layer MPC tracks the 22 °C reference most closely (mean RMSE 0.017 °C versus 0.345 °C for HMPC), but HMPC, by letting the temperature float within the permitted band, uses 2.6% less simulated HVAC energy on average (2.0–3.9% across scenarios). Mean quadratic-programming solution times of about 1.8 ms (upper layer) and 1.2 ms (lower layer) point to a low computational burden. The results quantify a trade-off between tracking precision and energy use; experimental validation with measured building data is left for future work................. Keywords:............... Building energy management, Energy efficiency, Hierarchical model predictive control, HVAC systems, Temperature-band compliance.