This work introduces a new finite element method for the modeling of the transient thermal behavior of mediums containing thin layers such as adhesive joints without any required mesh refinement in their vicinity. The methodology is based on the recent MAX-FEM model introduced in a previous authors' work. This model consists in correcting the classical Finite Element Method (FEM) by correction matrices taking into account the presence of thin layers without any mesh refinement. The proposed correction is issued from an analytical approach based on Matching Asymptotic Expansions (MAE) and by pretending the principle of the numerical eXtended Finite Elements Method (X-FEM). To describe the thermal behavior of 1D-adhesively bonded structures, the developed hybrid model has been implemented under Matlab code to perform transient explicit analyses. The efficiency of the model is then systematically tested in terms of time computation. All the derived results are compared to FEM, and some proposed applications deal with harmful conditions, material properties or specific boundary layers such as coating systems.