A possible source of $gamma$-ray photons observed from the jets of blazars is inverse Compton scattering by relativistic electrons of infrared seed photons from a hot, dusty torus in the nucleus. We use observations from the Spitzer Space Telescope to search for signatures of such dust in the infrared spectra of four $gamma$-ray bright blazars, the quasars 4C 21.35, CTA102, and PKS 1510$-$089, and the BL Lacertae object ON231. The spectral energy distribution (SED) of 4C 21.35 contains a prominent infrared excess indicative of dust emission. After subtracting a non-thermal component with a power-law spectrum, we fit a dust model to the residual SED. The model consists of a blackbody with temperature $sim1200$ K, plus a much weaker optically thin component at $sim660$ K. The total luminosity of the thermal dust emission is $7.9pm0.2 times 10^{45}$ erg s$^{-1}$. If the dust lies in an equatorial torus, the density of IR photons from the torus is sufficient to explain the $gamma$-ray flux from 4C 21.35 as long as the scattering occurs within a few parsecs of the central engine. We also report a tentative detection of dust in the quasar CTA102, in which the luminosity of the infrared excess is $7 pm 2 times 10^{45}$ erg s$^{-1}$. However, in CTA102 the far-IR spectra are too noisy to detect the $10 mu$m silicate feature. Upper limits to the luminosity from thermal emission from dust in PKS 1510-089, and ON231, are, $2.3times10^{45}$, and $6.6times10^{43}$ erg s$^{-1}$, respectively. These upper limits do not rule out the possibility of inverse Compton up-scattering of IR photons to $gamma$-ray energies in these two sources. The estimated covering factor of the hot dust in 4C 21.35, 22%, is similar to that of non-blazar quasars; however, 4C 21.35 is deficient in cooler dust.
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