This article addresses the plane strain problem of a bi-material system containing an elliptical cylindrical thermal inclusion. Using Eshelby’s inclusion analysis method, we derive closed-form analytical solutions for the elastic field induced by the thermal inclusion. Inspired by Dundurs’ parameters, we introduce a new material parameter (ranging from -1 to 1) and five tensorially structured expressions to succinctly represent the analytical solution, facilitating its practical applications. For circular inclusion scenarios, the analytical solution simplifies significantly, and we derive explicit jump conditions for displacement, strain, and stress at the bonded interface of the bi-material. By adjusting the Young’s moduli and Poisson’s ratios of the bi-material, the solution can reduce to cases of a full or half-plane containing a thermal elliptical inclusion. The accuracy of the proposed solution is validated through consistency with previously published analytical results and by matching numerical solutions from the literature, confirming the correctness and reliability of the derived analytical expressions.