We present SHARC-2 350 μm data on 20 luminous z ~ 2 starbursts with S 1.2 mm > 2 mJy from the Spitzer-selected samples of Lonsdale et al. and Fiolet et al. All the sources were detected, with S 350 μm > 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 6 μm-2 mm measurements of local starbursts. We find characteristic single-component temperatures T 1 ~= 35.5 ± 2.2 K and integrated infrared (IR) luminosities around 1012.9 ± 0.1 L sun for the SWIRE-selected sources. Molecular gas masses are estimated at sime4 × 1010 M sun, assuming κ850 μm = 0.15 m2 kg-1 and a submillimeter-selected galaxy (SMG)-like gas-to-dust mass ratio. The best-fit models imply gsim2 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 μm flux densities, provides an effective means for the study of SMGs at z ~ 1.5-2.5.