This paper presents a rational modelling procedure of a pilot heating process by using the grey box modelling method. A simplified nonlinear continuous model, based on the conservation of energy, is formed and unknown parameters of the model are estimated by using measured data from an experiment with the process. The model is expanded with a wider model structure by testing formulated hypothesis about the process. The model is also expanded in an engineering way by considering the shape of the residuals. During the model expansion the Likelihood ratio test is applied for falsification tests. The study uses the continuous model for both estimating the states of the process and controlling the system. A continuous-discrete extended Kalman filter estimates the model states and time varying disturbances. The model predictive controller is based on the continuous process model, but the optimisation of the control performance index is made at discrete sampling instances. The control law compensates for changing temperature references and compensate for varying load situations. Besides using the model for control purposes the case demonstrate the possibility of using the grey box modelling technique to estimate physical process parameters such as the thermal diffusivity of the process. (C) 2003 Elsevier Science Ltd. All rights reserved.