We present SHARC-II 350um imaging of twelve 24um-bright (F_24um > 0.8 mJy) Dust-Obscured Galaxies (DOGs) and CARMA 1mm imaging of a subset of 2 DOGs, all selected from the Bootes field of the NOAO Deep Wide-Field Survey. Detections of 4 DOGs at 350um imply IR luminosities which are consistent within a factor of 2 of expectations based on a warm dust spectral energy distribution (SED) scaled to the observed 24um flux density. The 350um upper limits for the 8 non-detected DOGs are consistent with both Mrk231 and M82 (warm dust SEDs), but exclude cold dust (Arp220) SEDs. The two DOGs targeted at 1mm were not detected in our CARMA observations, placing strong constraints on the dust temperature: T_dust > 35-60 K. Assuming these dust properties apply to the entire sample, we find dust masses of ~3x10^8 M_sun. In comparison to other dusty z ~ 2 galaxy populations such as sub-millimeter galaxies (SMGs) and other Spitzer-selected high-redshift sources, this sample of DOGs has higher IR luminosities (2x10^13 L_sun vs. 6x10^12 L_sun for the other galaxy populations), warmer dust temperatures (>35-60 K vs. ~30 K), and lower inferred dust masses (3x10^8 M_sun vs. 3x10^9 M_sun). Herschel and SCUBA-2 surveys should be able to detect hundreds of these power-law dominated DOGs. We use HST and Spitzer/IRAC data to estimate stellar masses of these sources and find that the stellar to gas mass ratio may be higher in our 24um-bright sample of DOGs than in SMGs and other Spitzer-selected sources. Although larger sample sizes are needed to provide a definitive conclusion, the data are consistent with an evolutionary trend in which the formation of massive galaxies at z~2 involves a sub-millimeter bright, cold-dust and star-formation dominated phase followed by a 24um-bright, warm-dust and AGN-dominated phase.
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