A follow-up survey using the Submillimetre High-Angular Resolution Camera (SHARC-II) at 350 μm has been carried out to map the regions around several 850-μm-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-μm flux densities for 24 850-μm sources, seven of which are detected at ≥2.5σ within a 10 arcsec search radius of the 850-μm positions. When results from the literature are included the total number of 350-μm 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 ≃ 9 ×10⁸Mꙩ), luminous (LFIR≃ 2 ×10¹² Lꙩ) star-forming galaxies with intrinsic dust temperatures of ≃35K and star formation rates of ≃400Mꙩ yrˉ¹. 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 28K with a few hotter. We also place new constraints on the 350-μm source counts, N₃₅₀(>25 mJy)~ 200–500 degˉ².