  This paper is devoted to study the thermal aspects of a photon gas within the
context of Planck-scale-modified dispersion relations. We study the spectrum of
radiation and the correction to the \textit{Stefan$-$Boltzmann} law in
different cases when the Lorentz symmetry is no longer preserved. Explicitly,
we examine two models within the context of CPT$-$even and CPT$-$odd sectors
respectively. To do so, three distinct scenarios of the Universe are
considered: the Cosmic Microwave Background (CMB), the electroweak epoch, and
the inflationary era. Moreover, the equations of state in these cases turn out
to display a dependence on Lorentz-breaking parameters. Finally, we also
provide for both theories the analyses of the Helmholtz free energy, the mean
energy, the entropy and the heat capacity.
