<p>Annular and annular sector plates play a critical structural role in a wide range of industrial applications—such as heat exchangers, nuclear reactors, gas turbines, and aerospace systems—where they are routinely subjected to combined mechanical and thermal loads that pose significant risks of structural failure. The purpose of this research is to investigate the thermal buckling response of functionally graded (FG) multilayered hybrid nanocomposite annular sector plates reinforced with carbon nanotubes (CNTs) and graphene platelets (GPLs). The effective mechanical, elastic, and physical properties of the composite structure are evaluated using a modified model derived from the Halpin–Tsai micromechanical framework, integrated with the rule of mixtures. The theoretical formulation is developed based on the first-order shear deformation theory, and the differential quadrature finite element method is utilized to derive the numerical solutions. Multiple nanofiller distribution patterns, such as uniform distribution and functionally graded arrangements (FG-X, FG-O, and FG-V), are investigated to determine the most effective layer grading strategy. To assess the accuracy of the proposed methodology, comparative analyses are performed against existing published findings. The results indicate that a proper piecewise functionally graded distribution of CNT and GPL nanofillers can enhance the thermal buckling load capacity by up to 35%. To comprehensively evaluate the thermal buckling stability of composite annular sector plate structures, the effects of various parameters—including the nanofiller distribution pattern, weight fractions of CNTs and GPLs, number of layers, volume fraction index for nonlinear gradation patterns, sector angle, radius ratio, thickness ratio, and boundary conditions—are thoroughly examined. The findings are systematically presented using detailed graphical representations, diagrams, and tabulated data.</p>