  The \textit{Spitzer}/Infrared Spectrograph spectra of three spectroscopically
anomalous galaxies (IRAS~F10398+1455, IRAS~F21013-0739 and SDSS~J0808+3948) are
modeled in terms of a mixture of warm and cold silicate dust, and warm and cold
carbon dust. Their unique infrared (IR) emission spectra are characterized by a
steep $\simali$5--8$\mum$ emission continuum, strong emission bands from
polycyclic aromatic hydrocarbon (PAH) molecules, and prominent silicate
emission. The steep $\simali$5--8$\mum$ emission continuum and strong PAH
emission features suggest the dominance of starbursts, while the silicate
emission is indicative of significant heating from active galactic nuclei
(AGNs). With warm and cold silicate dust of various compositions ("astronomical
silicate," amorphous olivine, or amorphous pyroxene) combined with warm and
cold carbon dust (amorphous carbon, or graphite), we are able to closely
reproduce the observed IR emission of these %spectroscopically anomalous
galaxies. We find that the dust temperature is the primary cause in regulating
the steep $\sim$5--8$\mum$ continuum and silicate emission, insensitive to the
exact silicate or carbon dust mineralogy and grain size $a$ as long as
$a\simlt1\mum$. More specifically, the temperature of the $\simali$5--8$\mum$
continuum emitter (which is essentially carbon dust) of these galaxies is
$\sim$250--400$\K$, much lower than that of typical quasars which is
$\sim$640$\K$. Moreover, it appears that larger dust grains are preferred in
quasars. The lower dust temperature and smaller grain sizes inferred for these
three galaxies compared with that of quasars could be due to the fact that they
may harbor a young/weak AGN which is not maturely developed yet.
