In this paper, the problem of fouling detection in a parallel flow heat exchanger is tackled. Because the behavior of a heat exchanger is governed by coupled partial differential equations, we suggest describing its dynamics by using a 2D linear time-invariant gray-box Roesser model. A non-linear optimization of a standard non-convex cost function is introduced to estimate the state-space matrices of the Roesser model, more specifically to estimate its physical parameters. After the parameter estimation, the output temperatures of the obtained model are compared to the output temperatures of the process and residuals are generated in order to detect a potential fouling. Numerical simulations illustrate the efficiency of this new fouling detection approach.