  A non-uniform temperature profile may generate a pure spin current in
magnetic films, as observed for instance in the spin Seebeck effect. In
addition, thermally induced elastic deformations may set in that could affect
the spin current. A self-consistent theory of the magnonic spin Seebeck effect
including thermally activated magneto-elastic effects is presented and
analytical expressions for the thermally activated deformation tensor and
dispersion relations for coupled magneto-elastic modes are obtained. We derived
analytical results for bulk (3D) systems and thin magnetic (2D) films.
  We observed that the displacement vector and the deformation tensor in bulk
systems decay asymptotically as $u\sim1/R^{2}$ and $\varepsilon\sim1/R^{3}$,
respectively, while the decays in thin magnetic films proceed slower following
$u\sim1/R$ and $\varepsilon\sim1/R^{2}$. The dispersion relations evidence a
strong anisotropy in the magnetic excitations. We observed that a thermoelastic
steady state deformation may lead to both an enchantment or a reduction of the
gap in the magnonic spectrum. The reduction of the gap increases the number of
magnons contributing to the spin Seebeck effect and offers new possibilities
for the thermoelastic control of the Spin Seebeck effect.
