Dust-obscured galaxies (DOGs) are an ultraviolet-faint, infrared-bright galaxy population that reside at z similar to 2 and are believed to be in a phase of dusty star-forming and active galactic nucleus (AGN) activity. We present far-infrared (far-IR) observations of a complete sample of DOGs in the 2 deg(2) of the Cosmic Evolution Survey. The 3077 DOGs have < z > = 1.9 +/- 0.3 and are selected from 24 mu m and r(+) observations using a color cut of r(+) -[24] >= 7.5 (AB mag) and S-24 >= 100 mu Jy. Based on the near-IR spectral energy distributions, 47% are bump DOGs (star formation dominated) and 10% are power-law DOGs (AGN-dominated). We use SPIRE far-IR photometry from the Herschel Multi-tiered Extragalactic Survey to calculate the IR luminosity and characteristic dust temperature for the 1572 (51%) DOGs that are detected at 250 mu m (>= 3 sigma). For the remaining 1505 (49%) that are undetected, we perform a median stacking analysis to probe fainter luminosities. Herschel-detected and undetected DOGs have average luminosities of (2.8 +/- 0.4) x 10(12) L-circle dot and (0.77 +/- 0.08) x 10(12) L-circle dot, and dust temperatures of (33 +/- 7) K and (37 +/- 5) K, respectively. The IR luminosity function for DOGs with S-24 >= 100 mu Jy is calculated, using far-IR observations and stacking. DOGs contribute 10%-30% to the total star formation rate (SFR) density of the universe at z = 1.5-2.5, dominated by 250 mu m detected and bump DOGs. For comparison, DOGs contribute 30% to the SFR density for all z = 1.5-2.5 galaxies with S-24 >= 100 mu Jy. DOGs have a large scatter about the star formation main sequence and their specific SFRs show that the observed phase of star formation could be responsible for their total observed stellar mass at z similar to 2.