<p>This study presents an advanced modeling and analysis approach for the thermal buckling and post-buckling behavior of functionally graded (FG) sandwich beams. Thermal buckling, a critical instability triggered by temperature variations, is particularly significant in structures experiencing differential thermal expansion or contraction. The proposed method integrates the radial point interpolation method (RPIM) with the Taylor series continuation technique, employing a consistent linearization framework based on Timoshenko beam theory. By combining RPIM interpolation with the asymptotic numerical method (ANM), the approach ensures high accuracy and computational efficiency across various boundary conditions, material gradations, and thermal loading scenarios. The study investigates four FG sandwich beam configurations under thermal loads. Results indicate that for a clamped–clamped (C–C) FG sandwich beam of Type-A, the critical buckling temperature increases from 213.2 K (for a core thickness ratio of 1-0-1) to 283.9 K (for 1-4-1), demonstrating the influence of core thickness. In contrast, for a clamped–simply supported (C–S) Type-A beam, the critical temperature increases from 109.4 to 145.8 K with core thickness variation. Additionally, the proposed RPIM approach provides convergence with an error of less than 3.8% compared to finite element solutions, significantly reducing computational cost. The findings underscore the impact of material gradation and boundary conditions on the thermal stability of FG sandwich beams, offering valuable insights for advanced structural applications. The reliability and robustness of the proposed approach are validated through numerical examples, providing critical insights into the thermal buckling loads of FG sandwich beams under different boundary conditions.</p>