  The realization of single-molecule thermal conductance measurements has
driven the need for theoretical tools to describe conduction processes that
occur over atomistic length scales. In macroscale systems, the principle that
is typically used to understand thermal conductivity is Fourier's law. At
molecular length scales, however, deviations from Fourier's law are common in
part because microscale thermal transport properties typically depend on the
complex interplay between multiple heat conduction mechanisms. Here, the
thermal transport properties that arise from electron transfer across a thermal
gradient in a molecular conduction junction are examined theoretically. We
illustrate how transport in a model junction is affected by varying the
electronic structure and length of the molecular bridge in the junction as well
as the strength of the coupling between the bridge and its surrounding
environment. Three findings are of note: First, the transport properties can
vary significantly depending on the characteristics of the molecular bridge and
its environment; second, the system's thermal conductance commonly deviates
from Fourier's law; and third, in properly engineered systems, the magnitude of
electron hopping thermal conductance is similar to what has been measured in
single-molecule devices.
