  We present SHARC-2 350 micron data on 20 luminous z ~ 2 starbursts with
S(1.2mm) > 2 mJy from the Spitzer-selected samples of Lonsdale et al. and
Fiolet et al. All the sources were detected, with S(350um) > 25 mJy for 18 of
them. With the data, we determine precise dust temperatures and luminosities
for these galaxies using both single-temperature fits and models with power-law
mass--temperature distributions. We derive appropriate formulae to use when
optical depths are non-negligible. Our models provide an excellent fit to the
6um--2mm measurements of local starbursts. We find characteristic
single-component temperatures T1 ~ 35.5+-2.2 K and integrated infrared (IR)
luminosities around 10^(12.9+-0.1) Lsun for the SWIRE-selected sources.
Molecular gas masses are estimated at 4 x 10^(10) Msun, assuming
kappa(850um)=0.15 m^2/kg and a submillimeter-selected galaxy (SMG)-like
gas-to-dust mass ratio. The best-fit models imply >~2 kpc emission scales. We
also note a tight correlation between rest-frame 1.4 GHz radio and IR
luminosities confirming star formation as the predominant power source. The
far-IR properties of our sample are indistinguishable from the purely
submillimeter-selected populations from current surveys. We therefore conclude
that our original selection criteria, based on mid-IR colors and 24 um flux
densities, provides an effective means for the study of SMGs at z ~ 1.5--2.5.
