  We present deep Chandra observations and Spitzer Space Telescope infrared
(IR) spectroscopy of the shell in the composite supernova remnant (SNR) Kes 75
(G29.7-0.3). The remnant is composed of a central pulsar wind nebula and a
bright partial shell in the south that is visible at radio, IR, and X-ray
wavelengths. The X-ray emission can be modeled by either a single thermal
component with a temperature of ~ 1.5 keV, or with two thermal components with
temperatures of 1.5 and 0.2 keV. Previous studies suggest that the hot
component may originate from reverse-shocked SN ejecta. However, our new
analysis shows no definitive evidence for enhanced abundances of Si, S, Ar, Mg,
and Fe, as expected from supernova (SN) ejecta, or for the IR spectral
signatures characteristic of confirmed SN condensed dust, thus favoring a
circumstellar or interstellar origin for the X-ray and IR emission. The X-ray
and IR emission in the shell are spatially correlated, suggesting that the dust
particles are collisionally heated by the X-ray emitting gas. The IR spectrum
of the shell is dominated by continuum emission from dust with little, or no
line emission. Modeling the IR spectrum shows that the dust is heated to a
temperature of ~ 140 K by a relatively dense, hot plasma, that also gives rise
to the hot X-ray emission component. The density inferred from the IR emission
is significantly higher than the density inferred from the X-ray models,
suggesting a low filling factor for this X-ray emitting gas. The total mass of
the warm dust component is at least 0.013 solar masses, assuming no significant
dust destruction has occurred in the shell. The IR data also reveal the
presence of an additional plasma component with a cooler temperature,
consistent with the 0.2 keV gas component. Our IR analysis therefore provides
an independent verification of the cooler component of the X-ray emission.
