For several years, Model Predictive Control (MPC) is depicted in the literature as a promising way to increase buildings' energy efficiency during operation. This model-based control technique uses the optimal control theory to provide a constraint compliant, anticipative control, maximizing performance criteria. However, building and calibrating a reliable model for a real application is difficult, costly and time-consuming. Indeed, it requires hard expert work to retrieve all the building's data and tune the corresponding model. This prevents MPC to be widespread in Building Management Systems. In this paper, we propose a MPC formulation where all the optimization problems included in a MPC strategy (calibration, estimation, optimal control) are performed efficiently using gradient-based techniques and adjoint-based gradient computations. This formulation relies on an automated "white-box" modeling technique (with partial-differential equations) using Building Information Model (BIM - using gbXML standard here) files parsing. We also show that making extensive use of adjoint models in MPC opens opportunities for fast sensitivity analysis, which can, for instance, help to choose which parameters to calibrate.