  In this work, we examine the finite temperature properties of the CPT-even
and Lorentz-invariance-violating (LIV) electrodynamics of the standard model
extension, represented by the term $W_{\alpha \nu \rho \phi}F^{\alpha
\nu}F^{\rho \phi}$. We begin analyzing the hamiltonian structure following the
Dirac's procedure for constrained systems and construct a well-defined and
gauge invariant partition function in the functional integral formalism. Next,
we specialize for the non-birefringent coefficients of the tensor $W_{\alpha
\nu \rho \phi}$. In the sequel, the partition function is explicitly carried
out for the parity-even sector of the tensor $W_{\alpha \nu \rho \phi}$. The
modified partition function is a power of the Maxwell's partition function. It
is observed that the LIV coefficients induce an anisotropy in the black body
angular energy density distribution. The Planck's radiation law, however,
retains its frequency dependence and the Stefan-Boltzmann law keeps the usual
form, except for a change in the Stefan-Boltzmann constant by a factor
containing the LIV contributions.
