The general analysis of transformation group method has been developed to study the linear thermoelastic system. The application of one-parameter group reduces the number of independent variables. Consequently, the governing system of second-order partial differential equations reduced into systems of ordinary differential equations. In this paper some of these systems are solved analytically.The general analysis of transformation group method has been developed to study the linear thermoelastic system. The application of one-parameter group reduces the number of independent variables. Consequently, the governing system of second-order partial differential equations reduced into systems of ordinary differential equations. In this paper some of these systems are solved analytically.