Abstarct: The characteristics of porosity, auxeticity, and material heterogeneity of basic engineering structures (beams, sheets, and shells) have significant effects on their thermomechanical behavior. In addition, when such structures are subjected to transient hyperbolic heat conduction, their mathematical modeling and also the solution of the governing equations become very complicated. Therefore, in this research, the effect of heat wave propagation along with steady mechanical loads (transverse load and shear load) on the thermoelastic behavior of a circular plate of variable thickness made of two-directional porous-auxetic functionally graded material with a flexible support on an auxetic substrate is investigated. The plate material properties change in the thickness and radial directions in the form of continuous exponential functions. The investigated structure is placed on an elastic foundation consisting of an auxetic circular plate and a Winkler foundation. The mathematical model of the interaction between the main structure and the auxetic substrate is presented, and the effect of this interaction is considered as a vertical force on the plate. To predict the response of the structure to the applied loads, first, the non-Fourier heat conduction equation (Cattaneo-Vernotte model) is solved using the alternating-direction implicit finite difference method. Then, the system of the governing equations of the main structure, which were extracted baxsed on uncoupled thermoelasticity theory are solved using state-space and differential quadrature methods. The effect of key parameters on the heat wave propagation and oscillatory behavior of the temperature and also on the distribution of displacements, stresses and von Mises stress in the main sheet are evaluated. The results show that the inhomogeneity indices of the plate material and the thermal relaxation parameter play an important role in heat wave propagation. Also, the results display that the thermoelastic behavior of the non-homogeneous porous-auxetic circular plate is strongly influenced by the mentioned parameters and thermal shock coefficient. In addition to these, the results of this research lead the designer to design a non-homogeneous structure made of porous-auxetic mextamaterial with high auxeticity and low compressibility coefficient in interaction with an auxetic substrate with high auxeticity and a low Winkler stiffness coefficient.