This paper deals with the global modelling and the predictive functional control (PFC) of a tubular counter current heat exchanger. The hot product flowing through the inner tube is cooled and its outlet temperature is monitored under varying the flow rate of cold fluid circulating in the annular duct. A global model representing the response to inlet temperature variations is used to implement the PFC algorithm. The control law takes into account the convexity property of the heat exchanger, which distinguishes the linear effects of state perturbations from the non-linear effects of structure disturbances. The control equation corresponds to a generic algebraic solver, which enables to assess the inlet temperature or the flow rate of cold fluid. In this study, the manipulated variable used to control the heat exchanger is the flow rate of cold fluid corresponding to a parameter of the dynamic model while the inlet temperature, which is the principal input, is kept constant. The PFC algorithm is then 'parametric' and the manipulated parameter is derived from the control equation. The robustness of this controller has also been studied when inlet temperatures and flow rate of product are subjected to sudden fluctuations.