We present APEX SABOCA 350micron and LABOCA 870micron observations of 11 representative examples of the rare, extremely bright (S_1.4mm > 15mJy), dust-dominated millimeter-selected galaxies recently discovered by the South Pole Telescope (SPT). All 11 sources are robustly detected with LABOCA with 40 < S_870micron < 130mJy, approximately an order of magnitude higher than the canonical submillimeter galaxy (SMG) population. Six of the sources are also detected by SABOCA at >3sigma, with the detections or upper limits providing a key constraint on the shape of the spectral energy distribution (SED) near its peak. We model the SEDs of these galaxies using a simple modified blackbody and perform the same analysis on samples of SMGs of known redshift from the literature. These calibration samples inform the distribution of dust temperature for similar SMG populations, and this dust temperature prior allows us to derive photometric redshift estimates and far infrared luminosities for the sources. We find a median redshift of <z> = 3.0, higher than the <z> = 2.2 inferred for the normal SMG population. We also derive the apparent size of the sources from the temperature and apparent luminosity, finding them to appear larger than our unlensed calibration sample, which supports the idea that these sources are gravitationally magnified by massive structures along the line of sight.
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