The steady decrease of the feature size of integrated circuits towards the nanometer scale leads to an increase in generated heat per unit area. Hence, efficient transfer of heat away from hotspots of integrated circuits becomes a crucial issue in the design of new generations of electronic devices. The importance of efficient thermal transport is even more pronounced in moving parts of nanoelectromechanical systems (NEMS). Recent research has shown that low-dimensional nanomaterials possess high thermal conductivity and hence are promising candidates for efficient heat reduction in nanodevices. In this talk, we present results of theoretical modeling of heat transport in one-dimensional (e.g. long chain molecules) and
quasi-one-dimensional (e.g. carbon nanotubes) nanostructures. The study is performed under the assumption that the contribution of
electrons to thermal conductivity is negligible and therefore the heat transfer is solely due to nonlinear interactions between vibrations of atoms in a nanostructure. We investigate the role of various lattice vibration modes in the heat transport with a particular focus on nonlinear localized vibration modes (breathers). These modes are highly localized and have properties qualitatively different from the linear phonon vibration modes. In particular, breathers are very stable and, at certain conditions, they move at a constant velocity which exceeds the speed of sound. This property of breathers suggests their potential use in efficient transfer of heat away from hotspots in a nanoscopic device.