This paper deals with an observer built for distributed parameter systems described by bilinear representation. The estimator is based on combination of the Luenberger's observer extension and the MacCormack's numerical method for resolution of the partial differential equations. This technique consists on distributing the state in a suite of vectors called partial states, which are estimated using a predictor and a corrector. The iterative predictor scans the distributed system to evaluate its internal states and the corrector scans backward to adjust the states estimation. The order of the partial state matrix remains unchanged while the state vector order increases according to the spatial discretisation step. Furthermore, this observer is applied to a coaxial counter current heat exchanger in order to estimate the temperatures of the two fluids and the separating wall, under varying liquids flow rates. This observer is experimentally validated for different positions along the counter current heat exchanger.