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We present N₂D⁺ 3-2 (IRAM), and H₂D⁺ 1₁₁-1₁₀ 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 H₂column 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≳ fewx10^–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.