A possible source of Delta *g-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 Delta *g-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 ~1200 K, plus a much weaker optically thin component at ~660 K. The total luminosity of the thermal dust emission is 7.9 ? 0.2 X 1045 erg s--1. If the dust lies in an equatorial torus, the density of infrared photons from the torus is sufficient to explain the Delta *g-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 ? 2 X 1045 erg s--1. However, in CTA102 the far-infrared spectra are too noisy to detect the 10 Delta *mm silicate feature. Upper limits to the luminosity from thermal emission from dust in PKS 1510--089, and ON231, are 2.3 X 1045, and 6.6 X 1043 erg s--1, respectively. These upper limits do not rule out the possibility of inverse Compton upscattering of infrared photons to Delta *g-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.