  In this work, we analyze the thermodynamic properties of the graviton and the
generalized model involving anisotropic Podolsky and Lee$-$Wick terms with
Lorentz violation. We build up the so-called partition function from the
accessible states of the system seeking the following thermodynamic functions:
spectral radiance, mean energy, Helmholtz free energy, entropy and heat
capacity. Besides, we verify that, when the temperature rises, the spectral
radiance $\chi(\nu)$ tends to attenuate for fixed values of $\xi$. Notably,
when parameter $\eta_{2}$ increases, the spectral radiance
$\bar{\chi}(\eta_{2},\nu)$ weakens until reaching a flat characteristic.
Finally, for both theories, we perform the calculation of the modified black
body radiation and the correction to the $\textit{Stefan-Boltzmann}$ law in the
inflationary era of the universe.
