This article deals with the transient thermoelastic analysis for dissimilar materials under the plane strain condition. In the process of the boundary element formulation, the time-dependent fundamental solution for the transient heat conduction problem and the thermoelastic displacement potential for the transient thermal stress problem are introduced. Consequently, domain integrals are completely eliminated. The discretization based on the domain combination method for these boundary integral equations is implemented, and the transient temperature and stress fields are analyzed numerically. The transient temperature at the lateral surface and the transient thermal stress at the interface are investigated for the three categories that have been determined according to the characteristic equation expressed by Dundurs parameters.