In this paper, we consider a one-dimensional linear Timoshenko system of thermoelasticity type III and prove a polynomial stability result for the non-equal wave-propagation speed case. Mathematics Subject Classification 35B37 • 35L55 • 74D05 • 93D15 • 93D20 1 Introduction A simple model describing the transverse vibration of a beam, which has the form ⎧ ⎨ ⎩ ρu tt = (K (u x − ϕ)) x , in (0, L) × (0, +∞) I ρ ϕ tt = (E I ϕ x) x + K (u x − ϕ), in (0, L) × (0, +∞), (1.1) was developed by Timoshenko [24], where t denotes the time variable and x is the space variable along the beam of length L , in its equilibrium configuration, u is the transverse displacement of the beam and ϕ is the rotation angle of the filament of the beam. The coefficients ρ, I ρ , E, I and K are respectively the density (the mass per unit length), the polar moment of inertia of a cross section, Young's modulus of elasticity, the moment of inertia of a cross section, and the shear modulus. Many researchers got interested in studying (1.1) and various damping mechanisms have been used to stabilize the vibrations of this system. The obtained results show that the presence of dissipation for both equations leads to uniform stability (exponential or polynomial) regardless to the values of the constants ρ, I ρ , E, I and K. This has been demonstrated by Kim and Renardy [10], Feng et al. [3], Raposo et al. [21], Santos [22], Messaoudi and Mustafa [11] and others.