The formalism for a linear-response many-body treatment of the electronic
contributions to thermal transport is developed for multilayered
nanostructures. By properly determining the local heat-current operator, it is
possible to show that the Jonson-Mahan theorem for the bulk can be extended to
inhomogeneous problems, so the various thermal-transport coefficient integrands
are related by powers of frequency (including all effects of vertex corrections
when appropriate). We illustrate how to use this formalism by showing how it
applies to measurements of the Peltier effect, the Seebeck effect, and the
thermal conductance.Comment: 17 pages, 4 figures, submitted to Phys. Rev.