  Characterization of the relatively poorly-understood progenitor systems of
Type Ia supernovae is of great importance in astrophysics, particularly given
the important cosmological role that these supernovae play. Kepler's Supernova
Remnant, the result of a Type Ia supernova, shows evidence for an interaction
with a dense circumstellar medium (CSM), suggesting a single-degenerate
progenitor system. We present 7.5-38 $\mu$m infrared (IR) spectra of the
remnant, obtained with the {\it Spitzer Space Telescope}, dominated by emission
from warm dust. Broad spectral features at 10 and 18 $\mu$m, consistent with
various silicate particles, are seen throughout. These silicates were likely
formed in the stellar outflow from the progenitor system during the AGB stage
of evolution, and imply an oxygen-rich chemistry. In addition to silicate dust,
a second component, possibly carbonaceous dust, is necessary to account for the
short-wavelength IRS and IRAC data. This could imply a mixed chemistry in the
atmosphere of the progenitor system. However, non-spherical metallic iron
inclusions within silicate grains provide an alternative solution. Models of
collisionally-heated dust emission from fast shocks ($>$ 1000 km s$^{-1}$)
propagating into the CSM can reproduce the majority of the emission associated
with non-radiative filaments, where dust temperatures are $\sim 80-100$ K, but
fail to account for the highest temperatures detected, in excess of 150 K. We
find that slower shocks (a few hundred km s$^{-1}$) into moderate density
material ($n_{0} \sim 50-250$ cm$^{-3}$) are the only viable source of heating
for this hottest dust. We confirm the finding of an overall density gradient,
with densities in the north being an order of magnitude greater than those in
the south.
