This manuscript examines the propagation of waves in a coaxial hollow infinite isotropic cylinder when exposed to a thermal heating source from the outer cylinder. For the mechanical conditions, the inner and outer cylinders are assumed to be displacement-free, in addition to a perfectly welded interface; while an insulation thermal condition is assumed on the interface to prevent the inner cylinder from being heated by an already-heated outer cylinder. Equally, a situation of an external load on the outer cylinder is also examined. As for the methodology, a mixture of the normal mode analysis method and the numerical Laplace integral transform is employed to study the vibrational displacements in the inner and outer cylinders, as well as the temperature field in the outer cylinder. Lastly, certain graphical illustrations associated with low and higher heating periods are demonstrated after considering some physical data and heating sources of practical application.