  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.
