The analysis of a critical buckling temperature is dependent on the new displacement function field provided in the literature and uses third-order shear deformation theory. The value of the parameter “m,” which determines the new displacement function, closed with the three-dimensional (3D) elasticity results. Thermal critical buckling is analyzed for thick and thin laminated plates by using the Navier solution for symmetric and anti-symmetric cross-ply simply supported boundary conditions. Several design parameters are considered such as extension thermal coefficient ratio (α
1⁄α
2), number of schemes, thickness ratio (a/h), aspect ratio (a/b), and modular ratio (E
1/E
2) when analyzing the dynamic behavior of the critical buckling temperature for different materials, including composite (glass/epoxy) and hybrid (glass/carbon/epoxy), under uniformly distributed temperature load. The accuracy for theoretical results by using Matlab R2019b was checked with other results for different researchers and gave good agreement. Increasing orthotropic ratio and aspect ratio resulted in increasing critical buckling temperature in M1 than M2, whereas increasing thickness ratio, thermal coefficient expansion, and number of layers resulted in decrease in critical buckling temperature in M2 than M1.