  Inelastic tunneling of electrons can generate the emission of photons with
energies intuitively limited by the applied bias voltage. However, experiments
indicate that more complex processes involving the interaction of electrons
with plasmon polaritons lead to photon emission with overbias energies. We
recently proposed a model of this observation in Phys. Rev. Lett. \textbf{113},
066801 (2014), in analogy to the dynamical Coulomb blockade, originally
developed for treating the electromagnetic environment in mesoscopic circuits.
This model describes the correlated tunneling of two electrons interacting with
a local plasmon-polariton mode, represented by a resonant circuit, and shows
that the overbias emission is due to the non-Gaussian fluctuations. Here we
extend our model to study the overbias emission at finite temperature. We find
that the thermal smearing strongly masks the overbias emission. Hence, the
detection of the correlated tunneling processes requires temperatures $k_BT$
much lower than the bias energy $eV$ and the plasmon energy $\hbar\omega_0$, a
condition which is fortunately realized experimentally.
