<p>This paper presents a novel and efficient investigation into the thermal buckling behavior of tri-directional functionally graded material (TDFGM) plates under uniform temperature rise. Different from traditional functionally graded materials with unidirectional or bidirectional variations, the material properties of this plate, such as Young’s modulus and coefficient of thermal expansion, vary continuously in all three spatial coordinate directions (the thickness direction and two in-plane directions), offering greater design flexibility for extreme thermal environments. The Reddy’s third-order shear deformation theory (TSDT) is employed to accurately describe the displacement field. The governing equations are derived based on the principle of minimum potential energy. The Chebyshev–Ritz method is utilized for an efficient numerical solution. The displacement components are expanded using Chebyshev polynomials multiplied by appropriate boundary functions to strictly satisfy clamped boundary conditions. The reliability of this method is verified through convergence studies. Comprehensive validation is carried out by comparing the obtained solutions of the critical buckling temperature with existing ones. A parametric study systematically explores the significant influence of the gradient index, aspect ratio, and thickness of the plate on the thermal buckling response. The results indicate that customizing the three-dimensional material gradient plays a crucial role in controlling the thermal stability of advanced composite plates.</p>