Many attempts have been made to investigate the classical heat transfer of Fourier, and a
number of improvements have been implemented. In this work, we consider a novel thermoelasticity
model based on the Moore–Gibson–Thompson equation in cases where some of these models fail to
be positive. This thermomechanical model has been constructed in combination with a hyperbolic
partial differential equation for the variation of the displacement field and a parabolic differential
equation for the temperature increment. The presented model is applied to investigate the wave
propagation in an isotropic and infinite body subjected to a continuous thermal line source. To solve
this problem, together with Laplace and Hankel transform methods, the potential function approach
has been used. Laplace and Hankel inverse transformations are used to find solutions to different
physical fields in the space–time domain. The problem is validated by calculating the numerical
calculations of the physical fields for a given material. The numerical and theoretical results of other
thermoelastic models have been compared with those described previously.