A three-dimensional problem for a homogeneous isotropic thermo-elastic half-space subjected to a time-dependent heat source on the boundary of the space, which is traction free, is considered in the context of the Green and Naghdi model II and III (without energy dissipation and with energy dissipation, respectively) of generalized thermo-elasticity. Normal mode analysis and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled field equations. Numerical results for the real parts of the temperature, thermal stresses, and displacement distributions are presented graphically and we analyze the obtained results in various cases-(i) for different values of the space variables; (ii) for different values of the time instant, and (iii) for different values of the Green-Naghdi parameter. Comparisons are made with the results for the real parts of the temperature, thermal stresses, and displacement distributions predicted by the Green-Naghdi model II and Green-Naghdi model III in these cases also. © 2013 Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.