In this paper, our main goal is to study the stability of the ther-moelastic Timoshenko beam with locally distributed temperature. Then, we consider the transmission problem of the Timoshenko system in thermoelas-ticity with two concentrated masses. We show the non-exponential stability by using a result introduced by J. E. Muñoz Rivera and R. Racke [18] based on the Weyl theorem. Otherwise, we prove the polynomial stability by using a frequency domain method
