  We show that charge fluctuation processes are crucial for the nonlinear heat
conductance through an interacting nanostructure, even far from a resonance. We
illustrate this for an Anderson quantum dot accounting for the first two
leading orders of the tunneling in a master equation. The often made assumption
that off-resonant transport proceeds entirely by virtual occupation of charge
states, underlying exchange-scattering models, can fail dramatically for heat
transport. The identified energy-transport resonances in the Coulomb blockade
regime provide new qualitative information about relaxation processes, for
instance by strong negative differential heat conductance relative to the heat
current. These can go unnoticed in the charge current, making nonlinear
heat-transport spectroscopy with energy-level control a promising experimental
tool.
