The simulation of heat convection problems usually leads to very large matrix systems because both Navier–Stokes equations and the energy equations are to be taken into account and discretized. Of course, such large matrix systems cannot be used for on-line control algorithms due to memory limitations and computation time. On-line control algorithms should rather consider much smaller matrix systems. Bearing this in mind, model reduction techniques present a large interest to obtain a suitable low-order model that can further be used in control processes. In this paper, reduced models are obtained through the modal identification method. This method relies on the solution of an optimization problem of parameter estimation following the steps: (i) the structure of the state model is first defined, (ii) the related vectors and matrices are estimated through the minimization of a corresponding functional, (iii) the reduced order model then must be validated with input data different from those used within the identification process. These steps being completed, other control algorithms can “plug” such reduced models. Among linear control algorithms, the feedback control laws considered in this paper are based either on the reduced state or on the output. A Kalman filter evaluates the state through a limited number of measurements. The developed numerical application deals with a temperature field within a 2D stationary flow over a backward-facing step. The goal is to keep the outlet temperature as close as possible to a given temperature profile downstream from the step, whatever the pipe inlet temperature fluctuations. One thus searches some “optimal” heat fluxes upstream from the step that counteract the inlet temperature variations.