We present new, high angular resolution two-color maps of the compact H II region DR 21 at 50 mu m and 100 mu m made with the 0.91 m telescope of NASA's Kuiper Airborne Observatory (KAO). From the maps we estimate the total fluxes of DR 21 at 50 mu m and 100 mu m to be 1.5 x 10(4) Jy and 3.8 x 10(4) Jy, respectively. 1. A homogenous plane-parallel slab model (Model I) is assumed in order to derive dust temperatures and optical depths. This model implies that the dust in DR 21 has relatively small optical depths at 100 mu m (tau(100) similar to 0.1) and its temperature ranges from less than 20 K to similar to 55 K. 2. A second model is also presented (Model II): a spherically symmetric dust cloud surrounding an O6 star. We used the radiation transfer code developed by Egan, Leung, and Spagna (1988). Our selection criteria for the best fit were based on the best match for both the energy distribution in the 50-1300 mu m range and the 100 mu m source profile. Assuming the dust properties reported by Mathis, Mezger, & Panagia (1983), and using a mixture of graphite (50% by number) and silicate (50% by number), the best fit to the observations in our modeling with this approach is a spherical dust cloud described by an outer radius of 2.0 pc, an inner radius of 0.1 pc, and a constant dust density distribution. Although this model provides a reasonable fit to the 50-1300 mu m flux densities and a marginal fit to the 100 mu m profile, the predicted FWHM profiles at 800 and 1100 mu m are much broader than those observed with high angular resolution (15 '' and 19 '' beams, respectively) as reported in the available literature.