(abridged) We present the first study of the farIR properties of high redshift, radio-selected ULIRGs using deep observations obtained with SPIRE from the Herschel Multi-tiered Extragalactic Survey (HerMES). These galaxies span a large range of 850um fluxes from submillimetre-luminous ~10mJy SCUBA galaxies -- SMGs to ~1.5mJy from stacked SCUBA non-detections, thus likely representing a complete distribution of ULIRG spectral energy distributions. From Keck spectroscopic surveys in the Lockman-North field we identified a sample of 31 SMGs and 37 submillimetre-faint, optically-faint radio galaxies (OFRGs), all with radio-inferred IR luminosities >10^12 Lsun. These galaxies were cross-identified with SPIRE 250, 350 and 500um catalogs based on fluxes extracted at 24um positions in the SWIRE survey, yielding a sample of more than half of the galaxies well detected in at least two of the SPIRE bandpasses. By fitting greybody dust models to the SPIRE photometry together with SCUBA 850um measurements, we infer dust temperatures and far-infrared luminosities. The OFRGs detected by SPIRE have median <T_d>= 41+-5 K and the SMGs have <T_d>= 34+-5 K, both in reasonable agreement with previous (pre-Herschel) estimates, reaffirming that the local FIR/radio correlation holds (at least for this subset of high-z ULIRGs) at high redshift. Our observations firstly confirm that a substantial fraction of OFRGs exhibit large infrared luminosities corresponding to SFRs of ~400 Msun/yr. The SPIRE observations secondly confirm the higher dust temperatures for these OFRGs than similarly selected SMGs, consistent with early predictions of the submm-faint radio populations. Our observations also clearly confirm the large infrared luminosities of most SMGs selected with S850um>5 mJy and radio and strong 24um detections, corresponding to SFRs of ~700 Msun/yr.
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