We present a joint analysis of the overlapping BLAST 250 , 350 , 500 µm , and Large APEX Bolometer Camera 870 µm observations ( from the LESS survey ) of the Extended Chandra Deep Field South . Out to z \sim 3 , the BLAST filters sample near the peak wavelength of thermal far-infrared ( FIR ) emission from galaxies ( rest-frame wavelengths \sim 60 –200 µm ) , primarily produced by dust heated through absorption in star-forming clouds . However , identifying counterparts to individual BLAST peaks is very challenging , given the large beams ( FWHM 36–60 arcsec ) . In contrast , the ground-based 870 µm observations have a significantly smaller 19 arcsec FWHM beam , and are sensitive to higher redshifts ( z \sim 1 –5 , and potentially beyond ) due to the more favourable negative K -correction . We use the LESS data , as well as deep Spitzer and VLA imaging , to identify 118 individual sources that produce significant emission in the BLAST bands . We characterize the temperatures and FIR luminosities for a subset of 69 sources which have well-measured submm SEDs and redshift measurements out to z \sim 3 . For flux-limited sub-samples in each BLAST band , and a dust emissivity index \beta = 2.0 , we find a median temperature T = 30 K ( all bands ) as well as median redshifts : z = 1.1 ( interquartile range 0.2–1.9 ) for S _ { 250 } > 40 mJy ; z = 1.3 ( interquartile range 0.6–2.1 ) for S _ { 350 } > 30 mJy ; and z = 1.6 ( interquartile range 1.3–2.3 ) for S _ { 500 } > 20 mJy . Taking into account the selection effects for our survey ( a bias toward detecting lower-temperature galaxies ) , we find no evidence for evolution in the local FIR-temperature correlation out to z \sim 2.5 . Comparing with star-forming galaxy SED templates , about 8 % of our sample appears to exhibit significant excesses in the radio and/or mid-IR , consistent with those sources harbouring an AGN . Since our statistical approach differs from most previous studies of submm galaxies , we describe the following techniques in two appendices : our ‘ matched filter ’ for identifying sources in the presence of point-source confusion ; and our approach for identifying counterparts using likelihood ratios . This study is a direct precursor to future joint far-infrared/submm surveys , for which we outline a potential identification and SED measurement strategy .