This article aims to investigate the wave propagation of generalized thermoelastic half-plane under the effect of thermal loading due to laser pulse with and without energy dissipation. The normal mode method is proposed to solve the problem and get numerical results for the field quantities. The outcomes of the physical quantities have been illustrated graphically and reported to compare the simple Green-Naghdi II and III and their modified single-, dual-, and three-phase-lag models. The graphical outcomes indicate that the different types of Green-Naghdi models with thermal relaxations have great effects on the temperature, displacements, dilatation and stresses.