  We study the flight time fluctuations of a probe light propagating in a slab
of nonlinear optical material with an effective fluctuating refractive index
caused by thermal fluctuations of background photons at a temperature $T$,
which are analogous to the lightcone fluctuations due to fluctuating spacetime
geometry when gravity is quantized. A smoothly varying second order
susceptibility is introduced, which results in that background field modes
whose wavelengths are of the order of the thickness of the slab give the main
contribution. We show that, in the low-temperature limit, the contribution of
thermal fluctuations to the flight time fluctuations is proportional to $T^4$,
which is a small correction compared with the contributions from vacuum
fluctuations, while in the high-temperature limit, the contribution of thermal
fluctuations increases linearly with $T$, which dominates over that of vacuum
fluctuations. Numerical estimation shows that, in realistic situations, the
contributions from thermal fluctuations are still small compared with that from
vacuum fluctuations even at room temperature.
