The high-pressure (HP) turbine and compressor blades are subjected to severe aero-thermal loads either caused by high inlet temperature resulting from the combustion chamber or by the shock wave at the blade surface. In this paper, a partitioned conjugate heat transfer (CHT) approach is used to assess 3D cases with high temperature gradient. On one hand, the high temperature resulting from the combustion chamber generates high azimuthal and radial non uniformities on the nozzle guide vane (NGV), known as hot streak. Since the engine efficiency is directly related to the turbine inlet temperature, manufacturers are seeking to improve thermal barrier coatings (TBC) to allow higher temperature. On the other hand, compressor rotor blades are also subjected to high thermal loads caused by the shock waves. Since the shock wave substantially contributes to the heat transfer, an accurate prediction of the wall temperature is thus required in order to properly estimate the rotor efficiency. However, the thermal load gradient caused by the hot streak, the use of thermal barrier coating or the shock wave have an impact on the overall computation stability. This paper assess the stability for a Dirichlet-Robin interface condition. Indeed an optimal relaxation parameter value is given for the Robin condition to provide a stable CHT computation. The impact on stability of the transient coupling time-step, the coupling frequency and the thermal conductivity is also assessed and the new transient coupling time-step defined allows to correctly stabilize the coupled simulation.