A dynamic theory is developed for thermoelastic anisotropic plates. The formulation is developed in the most general form for a triclinic plate with no material symmetry by including the interactions between mechanical and thermal variables. The order of the theory is kept arbitrary and by increasing it one can enlarge the frequency range of the theory as much as desired. For the assessment of the approximate theory, the dispersion of axial waves propagating in generally orthotropic plates is considered. The comparison with the exact data gives a good indication for the power of the approximate theory: the match between the exact and approximate dispersion curves is excellent even for a lower order theory.