Towards understanding the Planck thermal dust models
  Understanding the properties of dust emission in the microwave domain is an
important premise for the next generation of cosmic microwave background (CMB)
experiments, devoted to the measurement of the primordial $B$-modes of
polarization. In this paper, we compare three solutions to thermal dust
emission by the Planck Collaboration \cite{PlanckDust03,planck_16,planck_com}
to point out significant differences between their respective parameters (the
spectral index $\beta$, the optical depth $\tau$ and the dust temperature
$T_d$). These differences originate from e.g. the priors on the parameters or
the contribution of the Cosmic infrared background (CIB).
