<p>This exploration investigates the thermal- and post-buckling behavior of functionally graded material (FGM) laminate plates, comprising a polymer matrix reinforced with graphene nanoplatelets (GNPs). The key novelty of this investigation lies in applying the differential quadrature method (DQM) to analyze the thermal buckling behavior of these plates, marking the first use of this method for such a problem. Each layer of the laminates is assumed to have a uniform thickness, with the graphene nanoplatelet volume fraction varying across layers to achieve different distribution patterns. The laminates are reinforced with functionally graded arrangements designated as O, X, and U configurations. The formulas of motion are derived using the first-order shear deformation theory (FSDT) combined with the von Kármán nonlinear strain–displacement relationships. The thermal buckling behavior is analyzed through the differential quadrature technique. The adjusted Halpin–Tsai micromechanical scheme is employed to determine the equivalent elastic modulus, while the rule of mixtures is employed to derive the equivalent composite properties. The outcomes demonstrate that the X configuration of graphene nanoplatelets significantly enhances the buckling resistance of the plates. Additionally, the exploration examines the influence of key parameters, including the graphene nanoplatelet volume fraction, aspect ratio, and length-to-thickness ratio, on the thermal- and post-buckling performance of the laminate plates.</p>