The present work investigates the propagation of harmonic plane waves in an isotropic and homogeneous elastic medium that is rotating with uniform angular velocity by employing the two-temperature generalized thermoelasticity, recently introduced by Youssef (IMA Journal of Applied Mathematics, 71, 383-390, 2006). Dispersion relation solutions for longitudinal as well as transverse plane waves are obtained analytically. Asymptotic expressions of several important characterizations of the wave fields, such as phase velocity, specific loss, penetration depth, amplitude coefficient factor and phase shift of thermodynamic temperature are obtained for high frequency as well as low frequency values. A critical value of the two-temperature parameter for the low frequency case is obtained. Using Mathematica, numerical values of the wave fields at intermediate values of frequency and for various values of the twotemperature parameter are computed. A detailed analysis of the effects of rotation on the plane wave is presented on the basis of analytical and numerical results. An in-depth comparative analysis of our results with the corresponding results of the special cases of absence of rotation of the body and with the case of generalized thermoelasticity is also presented. The most significant points are highlighted.