<p>This study investigates the influence of variable thermal conductivity on a homogeneous, isotropic, axisymmetric cylindrical structure within the framework of the Moore–Gibson–Thompson model of generalized thermoelasticity. Several thermoelastic models are employed to analyze the primary field variables, including temperature distribution, displacement, and stress components. The governing equations are formulated and solved using harmonic time variations and Hankel transforms, yielding solutions in the transformed domain. The inverse Hankel transform is computed numerically using Romberg integration, enhanced by an extended Simpson’s one-third rule with extrapolation for improved accuracy. The resulting system of equations is solved using the Gauss elimination method under appropriate boundary conditions. Numerical results are illustrated graphically with respect to radial and axial positions, demonstrating the impact of variable thermal conductivity and the comparative behavior of different thermoelastic models.</p>