Heat diffusion in stratified materials with the layers running parallel to the main heat flux direction is analyzed with special emphasis on the temperature field near the boundaries. In a previous work, a semi-analytical general solution was proposed as an extension of the thermal quadrupole method for heat conduction in heterogeneous media. In this paper, the steady solution is separated into an homogenized transfer in series with a constriction term, and a conductive boundary layer is defined. The same decomposition method is implemented for the semi-infinite transient case, and some simplified models are obtained from asymptotic expansions. For long times, the transient averaged signal is found to be superposed to the steady constriction matrix effect. The main application is to better envision experimental temperature field analysis for thermal non-destructive evaluation methods.