Because of the high-dimensional nature of partial differential equations (PDEs), identifying accurate models of processes, the behaviour of which is governed by PDEs, is a challenging problem which still deserves a lot of attention. We address the problem of identifying a grey-box model of a heat exchanger by combining equation-error and output-error-based algorithms. First, in order to estimate rough but reliable values of the sought physical parameters characterising the heat exchanger behaviour, we use the interesting properties of the reinitialised partial moments (RPMs) developed initially for ordinary differential equations to deal with the problem of inaccessible partial derivatives of the PDE. Such an adaptation of the RPM features to PDEs leads to a direct continuous-time system identification problem for which convex least-squares solutions can be found. Second, thanks to a description of the heat exchanger dynamics with a 2D linear time-invariant Roesser model, the aforementioned rough estimates are used as reliable initial guesses for the nonlinear optimisation of a standard non-convex cost function introduced to estimate the state-space matrices of the Roesser model we want to identify. The efficiency of this two-step approach in terms of physical parameter estimation is validated through the simulation of a co-current flow heat exchanger.