"A follow-up survey using the Submillimetre High-Angular Resolution Camera (SHARC-II) at 350 \u03BCm has been carried out to map the regions around several 850-\u03BCm-selected sources from the Submillimetre HAlf Degree Extragalactic Survey (SHADES). These observations probe the infrared (IR) luminosities and hence star formation rates in the largest existing, most robust sample of submillimetre galaxies (SMGs). We measure 350-\u03BCm flux densities for 24 850-\u03BCm sources, seven of which are detected at \u22652.5\u03C3 within a 10 arcsec search radius of the 850-\u03BCm positions. When results from the literature are included the total number of 350-\u03BCm flux density constraints of SHADES SMGs is 31, with 15 detections. We fit a modified blackbody to the far-IR (FIR) photometry of each SMG, and confirm that typical SMGs are dust-rich (Mdust\u2243 9 \u00D7 108M\u2299), luminous (LFIR\u2243 2 \u00D7 1012L\u2299) star-forming galaxies with intrinsic dust temperatures of \u224335 K and star formation rates of \u2243400 M\u2299 yr\u22121. 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-\u03BCm source counts, N350(>25 mJy) \u223C 200-500 deg\u22122." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "The SCUBA HAlf Degree Extragalactic Survey - VI. 350-\u03BCm mapping of submillimetre galaxies" . . . . . . . .