It is noted that the study of linear and non-linear thermo-elasticity systems has a key role inthermal conductivity, stresses, as well as elasticity, and temperature. The solution to these systemsis one of the important parts of the present research. The fractional form of various thermo-elasticsystems is discussed, and their solutions are attained in a sophisticated manner. The solutionsof fractional and integer thermo-elastic systems are further discussed via graphs and tables. Thegraphs have shown the closed contact between the exact and LRPSM solutions. For appropriatemodeling, the solutions of fractional problems are plotted and shown to be convergent towardsinteger-order problems solutions. From the tables, it is verified that as the terms of the obtained seriessolution increases, the higher accuracy is achieved quickly. The faster convergence and stability of thesuggested method supports its modification for other fractional higher non-linear complex systemsin nature.