  In this paper we study the one dimensional thermoelastic transmission problem
in a special string/beam structure: the two components are coupled at an
interface (identified to $0$). Either the string or the beam is supposed
thermoelastic, the heat flux is given by the Cattaneo's law instead of the
usual Fourier's law. We prove that the the energy decay of the whole system is
exponential if the string is thermoelastic. When only the beam is
thermoelastic, we prove that the energy of the coupling string/beam decays
polynomially to zero as $\frac{1}{t}$ and the decay rate can be, at most,
polynomially stable of order $\frac{1}{t^2}$.
