We present near-infrared spectroscopic observations from VLT ISAAC of thirteen 250 \mu m-luminous galaxies in the CDF-S , seven of which have confirmed redshifts which average to \langle z \rangle = 2.0 \pm 0.4 . Another two sources of the 13 have tentative z > 1 identifications . Eight of the nine redshifts were identified with H \alpha detection in H- and K-bands , three of which are confirmed redshifts from previous spectroscopic surveys . We use their near-IR spectra to measure H \alpha line widths and luminosities , which average to 415 \pm 20 km s ^ { -1 } and 3 \times 10 ^ { 35 } W ( implying SFR _ { H \alpha } \sim 200 M _ { \odot } yr ^ { -1 } ) , both similar to the H \alpha properties of SMGs . Just like SMGs , 250 \mu m-luminous galaxies have large H \alpha to far-infrared ( FIR ) extinction factors such that the H \alpha SFRs underestimate the FIR SFRs by \sim 8-80 times . Far-infrared photometric points from observed 24 \mu m through 870 \mu m are used to constrain the spectral energy distributions ( SEDs ) even though uncertainty caused by FIR confusion in the BLAST bands is significant . The population has a mean dust temperature of T _ { d } = 52 \pm 6 K , emissivity \beta = 1.73 \pm 0.13 , and FIR luminosity L _ { FIR } = 3 \times 10 ^ { 13 } L _ { \odot } . Although selection at 250 \mu m allows for the detection of much hotter dust dominated HyLIRGs than SMG selection ( at 850 \mu m ) , we do not find any \buildrel > \over { \sim } 60 K ‘ hot-dust ’ HyLIRGs . We have shown that near-infrared spectroscopy combined with good photometric redshifts is an efficient way to spectroscopically identify and characterise these rare , extreme systems , hundreds of which are being discovered by the newest generation of IR observatories including the Herschel Space Observatory .