Conjugate heat transfer procedures are commonly used in many scientific and aerospace problems in which accurate heat transfer predictions are needed. But these procedures may suffer from stability and performance limitations. This paper presents a numerical approach for steady conjugate heat transfer problems based on a stability analysis in a canonical coupling prototype. The main characteristics of the Dirichlet-Robin transmission procedure are presented and analyzed. Two fundamental parameters are introduced, a "numerical" Biot number controlling the stability process and an optimal coefficient that ensures unconditional stability and a high numerical efficiency of the coupled aerothermal simulations. An algorithm that chooses the locally most efficient numerical approach is proposed. An industrial test case then illustrates the excellent behavior of the interface treatments. Finally it is shown, on the basis of the numerical Biot number, that the choice of a relevant transmission condition is critically important in achieving an even faster convergence.