Robert Hooke is the first one who stated that "The power of any spring or elastic body is in the same proportion with the body’s extension" [1], while Cauchy who provided the governing equations of the linear theory of elasticity based on a fixed and known temperature (isothermal), and without any changes until now [2]. The problem of elasticity in a temperature transition is resolved at first by Duhamel. The conclusion deduced by Duhamel equations was repeated by Neumann, but in a different manner, it is considered the first theory of thermoelasticity, which is known as the uncoupled thermoelasticity theory. The first governing equation of this theory is the heat conduction equation (thermal equation), which is unrelated to the mechanical effect, while the second one is the equation of motion involves a known function of heat [3]. Danilovskaya was the first one who solved an actual problem based on thermoelasticity that is uncoupled with uniform heat. This hypothesis has two shortcomings. First, the hypothesis notes that the elastic body's mechanical condition has no impact on the temperature and does not conform to physical experiments. Second, the parabolic heat equation forecasts an infinite temperature spread speed, which contradicts again physical observations [3].