The present study is devoted to propagation of plane harmonic GNIII thermoelastic waves by the coupled system of linear equations of motion and heat transport based on the Green & Naghdi theory of thermoelasticity. Analytical findings and exact solutions are primarily related to complex wavenumbers, phase velocities and attenuation coefficients of the plane GNIII-thermoelastic waves. Complete analysis of all analytical branches of the wavenumbers is given.