A combination of proper orthogonal decomposition (POD) analysis and in situ adaptive tabulation (ISAT) is proposed for the representation of parameter-dependent solutions of coupled partial differential equation problems. POD is used for the low-order representation of the spatial fields and ISAT for the local representation of the solution in the design parameter space. The accuracy of the method is easily controlled by free threshold parameters that can be adjusted according to user needs. The method is tested on a coupled fluid-thermal problem: the design of a simplified aircraft air control system. It is successfully compared with the standard POD; although the POD is inaccurate in certain areas of the design parameters space, the PODISAT method achieves accuracy thanks to trust regions based on residuals of the fluid-thermal problem. The presented PODISAT approach provides flexibility, robustness and tunable accuracy to represent solutions of parametrized partial differential equations.