This paper deals with the thermoelastic interactions in a transversely isotropic, infinite hollow cylinder in which the boundaries are stress-free. There is no temperature in the inner boundary and heat flux is applied on the outer boundary. In the context of two-temperature generalized thermoelasticity theory, the three-phase-lag thermoelastic model and Green Naghdi model III (GN-III) are employed to study the thermophysical quantities. The Laplace transform is used to transform the coupled equations into the Laplace transformed domain. Then two different methods, the Galerkin finite element technique and eigen-value approach, are employed to solve the resulting equations in the transformed domain. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The physical quantities have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (GN-III and three-phase-lag model) and for two different methods are presented. © 2013 Copyright Taylor and Francis Group, LLC.