We present N2D+ 3-2 (IRAM) and H2D+ 1_11 - 1_10 and N2H+ 4-3 (JCMT) maps of the small cluster-forming Ophiuchus B2 core in the nearby Ophiuchus molecular cloud. In conjunction with previously published N2H+ 1-0 observations, the N2D+ data reveal the
deuterium fractionation in the high density gas across Oph B2. The average deuterium fractionation R_D = N(N2D+)/N(N2H+) ~ 0.03 over Oph B2, with several small scale R_D peaks and a maximum R_D = 0.1. The mean R_D is consistent with previous results in isolated starless and protostellar cores. The column density distributions of both H2D+ and N2D+ show no correlation with total H2 column density. We find, however, an anticorrelation in deuterium fractionation with proximity to the embedded protostars in Oph B2 to distances >= 0.04 pc. Destruction mechanisms for deuterated molecules require gas temperatures greater than those previously determined through NH3 observations of Oph B2 to proceed. We present temperatures calculated for the dense core gas through the equating of non-thermal line widths for molecules (i.e., N2D+ and H2D+) expected to trace the same core regions, but the observed complex line structures in B2 preclude finding a reasonable result in many locations. This method may, however, work well in isolated cores with less complicated velocity structures. Finally, we use R_D and the H2D+ column density across Oph B2 to set a lower limit on the ionization fraction across the core, finding a mean x_e, lim >= few x 10^{-8}. Our results show that care must be taken when using deuterated species as a probe of the physical conditions of dense gas in star-forming regions.
