  Thermal or chaotic light sources emit radiation characterized by a slightly
enhanced probability of emitting photons in bunches, described by a zero-delay
second-order correlation function $g^{(2)}(0) = 2$. Here we explore
photon-coincidence counting statistics of thermal cavities in the ultrastrong
coupling regime, where the atom-cavity coupling rate becomes comparable to the
cavity resonance frequency. We find that, depending on the system temperature
and coupling rate, thermal photons escaping the cavity can display very
different statistical behaviors, characterised by second-order correlation
functions approaching zero or greatly exceeding two.
