The theory of coupled thermoelastic plane strain wave propagation in an unbounded, periodically layered elastic plate is developed in terms of Floquet Waves. The dispersion spectrum is shown to be governed by the six roots of the dispersion relation which is presented in the form of a determinant of order twelve. The spectrum shows the typical band structure, consisting of stopping and passing bands, of wave propagation in a periodic medium. For the special case of wave propagation normal to the layering, the dispersion relation degenerates into the product of a fourth-order determinant and an eighth-order determinant. For the case of wave propagation at an arbitrary angle, it is shown that if there exists one coordinate system to impart symmetry to the structure, the dispersion relations along both ends of Brillouin zone can be factorized into the product of two determinants of order six. The significance of this uncoupling is examined.