A general solution to the field equations of a transversely isotropic thermoelastic without energy dissipation and with two temperatures due to various sources has been obtained in the transformed domain using the Laplace and Fourier transforms. As an application, concentrated or distributed sources have been taken to illustrate the utility of the approach. The transformed solutions are inverted numerically using a numerical inversion technique. The result in the form displacement components, conductive temperature and stress components are obtained numerically and illustrated graphically for particular model. Some special cases of interest are also discussed for investigation.