The purpose of the present study is to describe novel numerical coupling schemes to analyze the transient temperature field in a solid via a conjugate heat transfer procedure. Emphasis is put on the interfacial treatment based on two complementary treatments: Dirichlet-Robin and Neumann-Robin transmission conditions. The numerical methods are first presented on the basis of a stability analysis in an aerothermal model problem. Stability conditions are expressed and the mathematical expression of the most relevant coupling parameters are provided for the first time. Furthermore, an overview of all the coefficients that can be used in a transient thermally-coupled procedure are given and a unified approach for steady and unsteady ramps is proposed. Then, these interfacial schemes are applied to the problem of convective heat transfer over, and transient conduction heat transfer within, a flat plate. A comparative study with realistic operating conditions is carried out, at low and large Biot numbers. It is shown that certain choices of coupling coefficients, even if physically reasonable, may result in non converging algorithms. This confirms that a model problem provides insight to the behavior of complicated heat transfer cases and constitutes an invaluable aid for generating efficient interfacial schemes. Indeed, the numerical computations demonstrate the efficiency of the numerical schemes based on the main theoretical results. The trends predicted by the model problem are recovered and excellent convergence properties are observed in all cases. (C) 2017 Elsevier Ltd. All rights reserved.