  We examine the electronic heat transport phenomena in nanoscale junctions
composed of organic molecules coupled to two metallic reservoirs of different
temperatures. The electronic heat flux and its dynamical noise properties are
calculated within the scattering (Landauer) formalism with the transmission
probability determined by using non-equilibrium Green's functions (NEGF
technique). The method based on Taylor series expansion is used to determine
nonlinear corrections to the electronic heat flux and its noise power spectral
density with up to the second order terms with respect to the temperature
difference. Our results show only limited applicability of ballistic Fourier's
law and fluctuation-dissipation theorem to heat transport in molecular systems.
We derived and tested numerically several signal-signal, noise-signal, and
noise-noise relations applicable to nanoscale heat flow carried by electrons at
strongly non-equilibrium conditions (similar formulas are expected for phonons
and photons). Importantly, the special treatment proposed by us may be extended
to higher order terms in order to address a variety of problems related to
nonlinear thermal and electro-thermal effects which may occur at nanoscale.
