  One of the primary challenges facing upcoming CMB polarization experiments
aiming to measure the inflationary B-mode signal is the removal of polarized
foregrounds. The thermal dust foreground is often modeled as a single modified
blackbody, however overly simplistic foreground models can bias measurements of
the tensor-to-scalar ratio r. As CMB polarization experiments become
increasingly sensitive, thermal dust emission models must account for greater
complexity in the dust foreground while making minimal assumptions about the
underlying distribution of dust properties within a beam. We use Planck dust
temperature data to estimate the typical variation in dust properties along the
line of sight and examine the impact of these variations on the bias in r if a
single modified blackbody model is assumed. We then assess the ability of the
moment method to capture the effects of spatial averaging and to reduce bias in
the tensor-to-scalar ratio for different possible toy models of dust emission.
We find that the expected bias due to temperature variations along the line of
sight is significant compared to the target sensitivities of future CMB
experiments, and that the use of the moment method could reduce bias as well as
shed light into the distribution of dust physical parameters.
