  We use simple toy models of far-IR dust emission to estimate the accuracy to
which the polarization of the cosmic microwave background can be recovered
using multi-frequency fits, if the parametric form chosen for the fitted dust
model differs from the actual dust emission. Commonly used approximations to
the far-IR dust spectrum yield CMB residuals comparable to or larger than the
sensitivities expected for the next generation of CMB missions, despite fitting
the combined CMB + foreground emission to precision 0.1% or better. The
Rayleigh-Jeans approximation to the dust spectrum biases the fitted dust
spectral index by Delta beta_d = 0.2 and the inflationary B-mode amplitude by
Delta r = 0.03. Fitting the dust to a modified blackbody at a single
temperature biases the best-fit CMB by Delta r > 0.003 if the true dust
spectrum contains multiple temperature components. A 13-parameter model fitting
two temperature components reduces this bias by an order of magnitude if the
true dust spectrum is in fact a simple superposition of emission at different
temperatures, but fails at the level Delta r = 0.006 for dust whose spectral
index varies with frequency. Restricting the observing frequencies to a narrow
region near the foreground minimum reduces these biases for some dust spectra
but can increase the bias for others. Data at THz frequencies surrounding the
peak of the dust emission can mitigate these biases while providing a direct
determination of the dust temperature profile.
