Purpose <p>In the present paper, an advanced thickness-stretchable and higher-order model is extended for thermal and mechanical deformation/strain/stress analyses of composite graphene origami reinforced square plate subjected to thermal and mechanical loads. It is assumed that the model is manufactured from a Cu matrix including graphene origami.</p> Methods <p>The virtual work principle is employed to derive governing equations in terms of various displacement functions. Using an analytical method of the solution, the impact of folding, content and temperature is studied on the elasto-static responses.</p> Results <p>The numerical results are presented using the analytical method in terms of thermal loads, foldability parameter and graphene content.</p> Conclusions <p>An increase in deformation and stress is observed with an increase in foldability parameter and thermal loads.</p>