This article focuses on the analysis and solution of the plane strain problem of bi-material containing an elliptical cylindrical thermal inclusion. Following the inclusion analysis method proposed by Eshelby, we derive closed-form analytical solutions for the elastic field induced by an elliptical thermal inclusion. Inspired by Dundurs' parameters, we introduce a new material parameter (ranging from -1 to 1) and five tensorial structured expressions to succinctly represent the current analytical solution, facilitating practical applications. For typical circular inclusion problems, our analytical solution can be greatly simplified, and we derive jump conditions for displacement, strain, and stress at the bonded interface of the bi-material. By adjusting Young's moduli and Poisson's ratios of the bi-material, the current solutions can degenerate into analytical solutions for a full or half-plane containing a thermal elliptical inclusion. The consistency of these solutions with previously published analytical solutions for specific cases, along with the numerical solutions presented in this article matching those in the literature, confirms the correctness of the derived analytical solutions in this study.