The prediction of a building's thermal behaviour within a short time horizon is necessary in many energy management applications. A numerical model can serve this purpose provided a good accuracy is obtained through a suitable calibration procedure. The paper deals with a model calibration procedure based on short-time on-site and weather measurements. It builds upon optimal control theory: an adjoint model is introduced to derive the gradient of a least squares cost function at a low computational cost. Two problems are solved. The first one is a non-linear model training problem. It consists in identifying the main influencing parameters of the system of partial differential equations that form the tendency model. The second problem is a linear identification problem that consists in identifying the unknown internal gains. This second problem can be solved in real-time in a continuous monitoring process. Both problems are solved within the same framework and same tools, illustrating the efficiency of the optimal control tools in this context. We give simulation results that show the performance of the calibration procedure under uncertainties on input parameters.