The dynamic interaction of magneto-thermo-elastic waves in structural members of finite size is studied. Of special interest are the thermally induced small thickness vibrations in a planar conducting plate layer. To calculate the forced vibrations in the time domain, a modal expansion technique is proposed Therefore, the computation of the eigenvalues and eigenfunctions of the corresponding eigenvalue problem is the essential problem to be solved initially. In addition to a numerical evaluation of the algebraic eigenvalue equations, a perturbation analysis is presented to find the complex-valued eigensolutions of the problem for a weak coupling. In every case, the calculation of the forced vibrations is reduced to solving uncoupled ordinary differential equations. Finally, the complete thermally induced vibrations are represented by infinite series to be evaluated straightforwardly in a computer-aided form.