The model of generalized thermo-elastic plane waves under the effect of rotation is studied using the theory of thermo-elasticity recently proposed by Green and Lindsay. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, the displacement component and thermal stress. The resulting formulation is applied to two different concrete problems. The first deals with a thick plate subjected to a time-dependent heat source on each face. The second concerns the case of a heated punch moving across the surface of a semi-infinite thermo-elastic half-space subject to appropriate boundary conditions. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermo-elasticity with two relaxation times in the absence of rotation.