We present SHARC-II 350 \mu m imaging of twelve 24 \mu m-bright ( F _ { 24 \mu m } > 0.8 \ > mJy ) Dust-Obscured Galaxies ( DOGs ) and CARMA 1mm imaging of a subset of 2 DOGs . These objects are selected from the Boötes field of the NOAO Deep Wide-Field Survey . Detections of 4 DOGs at 350 \mu m imply infrared ( IR ) luminosities which are consistent to within a factor of 2 of expectations based on a warm dust spectral energy distribution ( SED ) scaled to the observed 24 \mu m flux density . The 350 \mu m upper limits for the 8 non-detected DOGs are consistent with both Mrk 231 and M82 ( warm dust SEDs ) , but exclude cold dust ( Arp 220 ) 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 \approx 3 \times 10 ^ { 8 } \ > M _ { \sun } . In comparison to other dusty z \sim 2 galaxy populations such as sub-millimeter galaxies ( SMGs ) and other Spitzer -selected high-redshift sources , this sample of DOGs has higher IR luminosities ( 2 \times 10 ^ { 13 } \ > L _ { \sun } vs . 6 \times 10 ^ { 12 } \ > L _ { \sun } for the other galaxy populations ) that are driven by warmer dust temperatures ( > 35-60 K vs . \sim 30 K ) and lower inferred dust masses ( 3 \times 10 ^ { 8 } \ > M _ { \sun } vs . 3 \times 10 ^ { 9 } \ > M _ { \sun } ) . Wide-field Herschel and SCUBA-2 surveys should be able to detect hundreds of these power-law dominated DOGs . We use existing Hubble Space Telescope 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 24 \mu m-bright sample of DOGs than in SMGs and other Spitzer -selected sources . Although much 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 \sim 2 involves a sub-millimeter bright , cold-dust and star-formation dominated phase followed by a 24 \mu m-bright , warm-dust and AGN-dominated phase .