  We study the finite temperature properties of the
Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics for a purely spacelike
background. Starting from the associated finite temperature partition function,
a modified black body spectral distribution is obtained. We thus show that, if
the CMB radiation is described by this model, the spectrum presents an
anisotropic angular energy density distribution. We show, at leading order,
that the Lorentz-breaking contributions for the Planck's radiation law and for
the Stefan-Boltzmann's law are nonlinear in frequency and quadratic in
temperature, respectively. Using our results, we set up bounds for the
Lorentz-breaking parameter, and show that Lorentz violation in the context of
the MCFJ model is unable to yield the known CMB anisotropy (of 1 part in
$10^{5})$.
