Better understanding and more accurate prediction of heat transfer and cooling flows in aero engine components in steady and transient operating regimes are essential to modern engine designs aiming at reduced cooling air consumption and improved engine efficiencies. This paper presents a simplified coupled transient analysis methodology that allows assessment of the aerothermal and thermomechanical responses of engine components together with cooling air mass flow, pressure and temperature distributions in an automatic fully integrated way. This is achieved by assembling a fluid network with contribution of components of different geometrical dimensions coupled to each other through dimensionally heterogeneous interfaces. More accurate local flow conditions, heat transfer and structural displacement are resolved on a smaller area of interest with multidimensional surface coupled CFD/FE codes. Contributions of the whole engine air-system are predicted with a faster mono dimensional flow network code. Matching conditions at the common interfaces are enforced at each time step exactly by employing an efficient iterative scheme. The coupled simulation is performed on an industrial high pressure turbine disk component run through a square cycle. Predictions are compared against the available experimental data. The paper proves the reliability and performance of the multidimensional coupling technique in a realistic industrial setting. The results underline the importance of including more physical details into transient thermal modelling of turbine engine components.