  In order to analyse classical electromagnetism in a medium at finite
temperature we introduce `an optical density operator', and reformulate
Maxwell's equations with the operator, starting from the Dirac-equation-like
formulation of electromagnetism. We find the thermal state of electromagnetic
field in the medium from the `optical Dirac Hamiltonian', which is the
effective Hamiltonian in the Dirac-like formulation. In the thermal state, the
two transverse modes (left-handed and right-handed circular polarisation) of
electromagnetic fields exist at the same ratio. We also analyse the asymptotics
of the thermal state. At the low temperature limit, there is correlation
between the electric field and the magnetic field. This means that there exists
an electromagnetic wave at the thermal equilibrium, and this recovers Maxwell's
classical electromagnetism. In contrast, the correlation vanishes at the high
temperature limit. This means that electromagnetic waves are unsustainable and
only independent electric fields and magnetic fields exist at the high
temperature limit.
