The appearance of the young supernova remnant SN 1006 is dominated by emission from nonradiative shocks in the northeast and northwest regions. At X-ray energies the northeast shock exhibits predominantly nonthermal synchrotron emission, while the northwest shock exhibits a thermal spectrum. We present far-ultraviolet spectra of the northeast (NE) and northwest (NW) portions of SN 1006 acquired with the Far Ultraviolet Spectroscopic Explorer (FUSE). We have detected emission lines of O VI λλ1032, 1038 and broad Lyβ λ1025 in the NW filament but detect no emission lines in the NE region down to a level of 4.7 × 10^-17 ergs cm^-2 s^-1 arcsec^-2. We observed in the NW an O VI intensity of 2.0 ± 0.2 × 10^-16 ergs cm^-2 s^-1 arcsec^-2 and measured an O VI line width of 2100 ± 200 km s^-1 at a position where the Hα width was measured to be 2290 ± 80 km s^-1. This implies less than mass-proportional heating of the ions. Using the ratio of intensities I(NW)/I(NE) ~ n(NW)/n(NE), the density ratio of the two regions is found to be ≥4, a value that is consistent with the uncertainties of the ratio of 2.5 measured in 2003 by Long and coworkers. The derived O VI kinetic temperature is compared to previous estimates of electron, proton, and ion temperatures in the remnant to study the relative heating efficiency of various species at the shock front. The degree of postshock temperature equilibration may be crucial to particle acceleration, since the temperature of each species determines the number of high-speed particles available for injection into an acceleration process that could produce Galactic cosmic rays.