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Electronic packages experience large temperature excursions during their fabrication and under operational conditions. Inherent to electronic packages are the presence of geometric and material discontinuities. The regions where adhesive bond lines intersect with convective heat-loss surfaces are the most critical locations for failure initiation due to heat flux singularities and extreme thermo-mechanical stresses. Thus, accurate calculation of the flux field, as well as the temperature field, is essential in transient thermo-mechanical stress analysis. Although the finite element method (FEM) is highly efficient and commonly used, its application with conventional elements suffers from poor accuracy in the prediction of the flux field in these regions. The accuracy of the results from the boundary element method (BEM) formulation, which requires computationally intensive time-integration schemes, is much higher than that of the FEM. However, in this study, a novel boundary element-finite element coupling algorithm is developed to investigate transient thermal responses of electronic packages consisting of dissimilar materials.