  In this paper, we investigate the stability of the transmission problem for
Rayleigh beam model with heat conduction. First, we reformulate our system into
an evolution equation and prove our problem's well-posedness. Next, we
demonstrate the resolvent of the operator is compact in the energy space, then
by using the general criteria of Arendt-Batty, we prove that the thermal
dissipation is enough to stabilize our model. Finally, a polynomial energy
decay rate has been obtained which depends on the mass densities and the
moments of inertia of the Rayleigh beams.
