  (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.
