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Advances in the fabrication and characterization of nanoscale systems now allow for a better understanding of one of the most basic issues in science and technology: the flow of heat at the microscopic level. In this Colloquium recent advances are surveyed and an understanding of physical mechanisms of energy transport in nanostructures is presented, focusing mainly on molecular junctions and atomic wires. Basic issues are examined such as thermal conductivity, thermoelectricity, local temperature and heating, and the relation between heat current density and temperature gradient---known as Fourier's law. Both theoretical and experimental progress are critically reported in each of these issues and future research opportunities in the field are discussed.
Dubi et al. (Mon,) studied this question.