A follow-up survey using the Submillimetre High-Angular Resolution Camera (SHARC-II) at 350 microns has been carried out to map the regions around several 850 micron-selected sources from the Submillimetre HAlf Degree Extragalactic Survey (SHADES). These observations probe the infrared luminosities and hence star-formation rates in the largest existing, most robust sample of submillimetre galaxies (SMGs). We measure 350 micron flux densities for 24 850 micron sources, seven of which are detected at >2.5-sigma within a 10 arcsec search radius of the 850 micron positions. When results from the literature are included the total number of 350 micron flux density constraints of SHADES SMGs is 31, with 15 detections. We fit a modified blackbody to the far-infrared (FIR) photometry of each SMG, and confirm that typical SMGs are dust-rich (Mdust~9x10^8 Msun), luminous (Lfir~2x10^12 Lsun), star-forming galaxies with intrinsic dust temperatures of ~35 K and star-formation rates of ~400 Msun/yr. We have measured the temperature distribution of SMGs and find that the underlying distribution is slightly broader than implied by the error bars, and that most SMGs are at 28 K with a few hotter. We also place new constraints on the 350 micron source counts, N350(>25mJy)~200-500 deg^-2.
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