In this work, a mathematical model of meshed plate nonlinear oscillations is constructed within the framework of a couple thermodynamics problem. The plate consists of an arbitrary number of densely spaced ribs families. Each family is characterized by the width of the family ribs, distance between the family ribs, and the inclination angle of the rib relative to the abscissa axis positive direction. The theory used in the work makes it possible to replace the ribs system with a continuous layer. The motion equations of plate element, boundary and initial conditions are obtained from the Hamilton’s variational principle by using Kirchhoff’s hypotheses. Geometric nonlinearity is taken into account according to the T von Karman’s theory. Scale effects are taken into account on the basis of the micropolar theory with constrained particles rotation. The Dugamel-Nemon’s hypothesis was taken into consideration. Three-dimensional hyperbolic type heat equation in a coupled formulation is considered. The heat equation is based on the Cattaneo-Vernot’s hypotheses. The carbon nanoplate nonlinear dynamics under the action of a temperature field and a vibrational normal load is investigated.