To study the heat transfer in ceramic coatings applied to the heated side of internally cooled hot section components of the gas turbine engine, a mathematical model is developed for the thermal response of plasma-sprayed ZrO2-Y2O3 ceramic materials with a Ni-Cr-AL-Y bond coat on a Rene 41 rod substrate subject to thermal cycling. This multilayered cylinder with temperature dependent thermal properties is heated in a cross-flow by a high velocity flame and then cooled by ambient air. Due to high temperature and high velocity of the flame, both gas radiation and forced convection are taken into consideration. Furthermore, the local turbulent heat transfer coefficient is employed which varies with angular position as well as the surface temperature. The transient two-dimensional (heat transfer along axial direction is neglected) temperature distribution of the composite cylinder is determined numerically.