A combination of Proper Orthogonal Decomposition (POD) and In Situ Adaptive Tabulation (ISAT) is proposed for the representation of parameter-dependent solutions of coupled partial differential equations (PDE). The accuracy of the method is easily controlled by open parameters that can be adjusted according to the users needs. The method is tested on a coupled fluid-thermal problem: the design of a simplified aircraft air control system. It is successfully compared to the standard POD: while the POD is inaccurate in certain areas of the design parameters space, the POD-ISAT method achieves accuracy thanks to residual based on trust regions. The presented POD-ISAT approach provides flexibility, robustness and tunable accuracy to represent solutions of parametrized PDEs.