This paper presents an overview analyses of the thermal instability or thermal viability of infinite cylindrical structures with non-linear and non-uniform internal heat generation. The structure may be subjected to different and combined boundary conditions. An analytical solution is obtained for the generalized problem in spite of the non- linearity and the non-homogeneity of the source term. Four case studies with different boundary conditions are presented. The analyses show that the critical parameter for thermal stability may be thought of as an altitude of surface below which the cylindrical structure will be thermally stable and performance worthy. The results also show that the bounds of thermal stability of a cylindrical structure system (solid or hollow) is eminently determined by the boundary conditions to which the system is subjected and can significantly alter the life-span of the structure.