We present follow-up observations to those of Geballe & Oka (2010), who found high column densities of H3+ ~100 pc off of the Galactic center (GC) on the lines of sight to 2MASS J17432173-2951430 (J1743) and 2MASS J17470898-2829561 (J1747). The wavelength coverages on these sightlines have been extended in order to observe two key transitions of H3+, R(3,3)l and R(2,2)l, that constrain the temperatures and densities of the environments. The profiles of the H3+ R(3,3)l line, which is due only to gas in the GC, closely matches the differences between the H3+ R(1,1)l and CO line profiles, just as it does for previously studied sightlines in the GC. Absorption in the R(2,2)l line of H3+ is present in J1747 at velocities between -60 and +100 km/s. This is the second clear detection of this line in the interstellar medium after GCIRS 3 in the Central Cluster. The temperature of the absorbing gas in this velocity range is 350 K, significantly warmer than in the diffuse clouds in other parts of the Central Molecular Zone. This indicates that the absorbing gas is local to Sgr B molecular cloud complex. The warm and diffuse gas revealed by Oka et al. (2005) apparently extends to ~100 pc, but there is a hint that its temperature is somewhat lower in the line of sight to J1743 than elsewhere in the GC. The observation of H3+ toward J1747 is compared with the recent Herschel observation of H2O+ toward Sgr B2 and their chemical relationship and remarkably similar velocity profiles are discussed.
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