Abstract <p>Equations describing the analytical dynamics of heterogeneous anisotropic thermoelastic plates are proposed. An <i>N</i>th-order model of the plate is determined by means of field variables—specifically, the coefficients in the expansion of the displacement and Biot entropy vectors in terms of the following functions: a biorthogonal basis system of functions of the normal coordinate; and the surface and contour densities of the Lagrange and Rayleigh functionals. The motion and heat transfer are described by generalized Lagrange equations of the second kind for a two-dimensional continuum system with dissipation.</p>