The linear Chen-Gurtin theory of heat conduction in deformable materials is used to study the propagation of one-dimensional harmonic waves in infinite media with thermal memory. A dispersion relation is derived and asymptotic dependences for phase velocities and damping coefficients of waves are investigated. As a result of the dispersion equation numerical solution, the frequency dependences of phase velocities and damping coefficients of thermoelastic waves are obtained and analyzed. It is shown that with allowance for the thermal memory (he solution yields increased velocities and enchanced damping of thermoelastic waves as compared to the Lord-Shulman generalized thermomechanical model (GT-model).