  Charge transfer is a fundamental process that underlies a multitude of
phenomena in chemistry and biology. Recent advances in observing and
manipulating charge and heat transport at the nanoscale, and recently developed
techniques for monitoring temperature at high temporal and spatial resolution,
imply the need for considering electron transfer across thermal gradients.
Here, a theory is developed for the rate of electron transfer and the
associated heat transport between donor-acceptor pairs located at sites of
different temperatures. To this end, through application of a generalized
multidimensional transition state theory, the traditional Arrhenius picture of
activation energy as a single point on a free energy surface is replaced with a
bithermal property that is derived from statistical weighting over all
configurations where the reactant and product states are equienergetic. The
flow of energy associated with the electron transfer process is also examined,
leading to relations between the rate of heat exchange among the donor and
acceptor sites as functions of the temperature difference and the electronic
driving bias. In particular, we find that an open electron transfer channel
contributes to enhanced heat transport between sites even when they are in
electronic equilibrium. The presented results provide a unified theory for
charge transport and the associated heat conduction between sites at different
temperatures.
