Background: Thermal barrier coatings are a promising concept to improve the lifetime of the copper liner of a rocket engine. Due to the high heat fluxes and the large thermal conductivity of copper, coatings have to be designed especially for this application. Methods: In this paper, we perform fully thermo-mechanically coupled finite element analyses of a small section of a combustion chamber with a coating system comprising a NiCuCrAl bond coat and a NiCrAlY top coat. Results: Heat fluxes are calculated to determine reasonable coating thickness values. Elastic and plastic deformation in the materials is considered to study the stress evolution. A crack model serves to estimate the possibility of vertical cracks propagating through the coating system. Conclusions: Several design guidelines are developed from these results that will aid future development of thermal barrier coatings.