In this paper, the problem of deriving a dynamical model of a cross flow heat exchanger is considered. In order to take into account the dependency of the system's dynamics on the hot and the cold mass flow rates in an explicit way, an input-output linear parameter-varying (LPV) model is used. A local approach composed of three steps is carried out to identify this LPV model. A parameter estimation scheme is introduced in which cost functions are minimized by using specific nonlinear programming methods. In this study, a finite volume physical model simulator is exploited to simulate and to generate the data. Simulations are performed to demonstrate the benefits of the suggested approach.