This article deals with the thermal vibration analysis of the graphene-oxide powder-reinforced (GOPR) nanocomposite plates, once the plate is embedded on the viscoelastic substrate. The structure is subjected to thermal loadings with various temperature rises such as sinusoidal temperature rise (STR), linear temperature rise (LTR), and uniform temperature rise (UTR). Damping behavior of the GOPR nanocomposite plates is investigated based on the variations of the natural frequencies. Four functionally graded (FG) patterns of GOPs’ distribution are taken into account comparatively in order to find out the best model of reinforcing the structure. The homogenization of the materials is carried based on the Halpin-Tsai micromechanical scheme. The governing equations of the motion have been derived through the combination of refined higher-order shear deformation theory and Hamilton’s principle. The accuracy of this modeling is validated with those reported in the open literature. Finally, the influences of different parameters on the natural frequencies of the embedded GOPR nanocomposite plates are investigated based on the damping coefficient of the viscoelastic substrate. The graphical results reveal that the free vibrational behavior of the structure is remarkably affected by the variations of these parameters. Communicated by Krzysztof Kamil Żur.