The cutout and temperature loading influences on the nonlinear frequencies of the laminated shell structures are predicted numerically using two different types of geometrical nonlinear strain-displacement relationships to count the large deformation. The displacement of any generic point on the structural panel is derived using the third-order shear deformation theory (TSDT). Moreover, the direct iterative method has been adopted to obtain the nonlinear eigenvalues in conjunction with the isoparametric finite element (FE) steps. The present analysis includes the effect of temperature and the temperature-dependent composite elastic properties on the thermoelastic frequencies. This study intends to establish the Green-Lagrange type of nonlinear strain's efficacy in computing the nonlinear frequency of layered structure with and without cutout instead of von-Karman strain kinematics. The numerical model's validity has been established by comparing the results to previously published results. In addition, experimentally obtained fundamental frequency values of a few modes are compared to numerical proposed numerical results under the thermal loading. Finally, the effects of cutout (shape and size) and the associated structural geometrical parameters on the nonlinear thermal frequency responses of the laminated structure are expressed in the final output form.