  Bose--Einstein condensation of a finite number of photons propagating inside
a plasma-filled microcavity is investigated. The nonzero chemical potential is
provided by the electrons, which induces a finite photon mass allowing
condensation to occur. We derive an equation that models the evolution of the
photon-mode occupancies, with Compton scattering taken into account as the
mechanism of thermalization. The kinetic evolution of the photon spectrum is
solved numerically, and we find evidences of condensation for realistic plasma
densities, $n_e\sim 10^{14} - 10^{15}\; \text{cm}^{-3}$, compatible with
microplasma technology. The critical temperature is almost linear in the number
of photons, and we find high condensate fractions at microcavity-plasma
temperatures, for experimentally reasonable cavity lengths ($ 100-500 \; \mu$m)
and photon numbers ($10^{10}-10^{12}$).
