  We develop a dynamical theory of heat transfer between two nano systems. In
particular, we consider the resonant heat transfer between two nanoparticles
due to the coupling of localized surface modes having a finite spectral width.
We model the coupled nanosystem by two coupled quantum mechanical oscillators,
each interacting with its own heat bath, and obtain a master equation for the
dynamics of heat transfer. The damping rates in the master equation are related
to the lifetimes of localized plasmons in the nanoparticles. We study the
dynamics towards the steady state and establish connection with the standard
theory of heat transfer in steady state. For strongly coupled nano particles we
predict Rabi oscillations in the mean occupation number of surface plasmons in
each nano particle.
