Despite the increasing capabilities of information technologies for data acquisition and processing, building energy management systems still require manual configuration and supervision to achieve optimal performance. Model predictive control (MPC) aims to leverage equipment control-particularly heating, ventilation, and air conditioning (HVAC)-by using a model of the building to capture its dynamic characteristics and to predict its response to alternative control scenarios. Usually, MPC approaches are based on simplified linear models, which support faster computation but also present some limitations regarding interpretability, solution diversification, and longer-term optimization. In this paper, we propose a novel MPC algorithm that uses a full-complexity grey-box simulation model to optimize HVAC operation in non-residential buildings. Our system generates hundreds of candidate operation plans, typically for the next day, and evaluates them in terms of consumption and comfort by means of a parallel simulator configured according to the expected building conditions (weather and occupancy). The system has been implemented and tested in an office building in Helsinki, both in a simulated environment and in the real building, yielding energy savings around 35% during the intermediate winter season and 20% in the whole winter season with respect to the current operation of the heating equipment.