In this work, we study the well‐posedness and the asymptotic stability of a one‐dimensional linear thermoelastic Timoshenko system, where the heat conduction is given by Cattaneo's law and the coupling is via the displacement equation. We prove that the system is exponentially stable provided that the stability number χτ=0. Otherwise, we show that the system lacks exponential stability. Furthermore, in the latter case, we show that the solution decays polynomially. Copyright © 2015 John Wiley & Sons, Ltd.