We measure H$_2$ temperatures and column densities across the Orion BN/KL explosive outflow from a set of thirteen near-IR H$_2$ rovibrational emission lines observed with the TripleSpec spectrograph on Apache Point Observatorys 3.5-meter telescope. We find that most of the region is well-characterized by a single temperature (~2000-2500 K), which may be influenced by the limited range of upper energy levels (6000-20,000 K) probed by our data set. The H$_2$ column density maps indicate that warm H$_2$ comprises 10$^{-5}$ - 10$^{-3}$ of the total H$_2$ column density near the center of the outflow. Combining column density measurements for co-spatial H$_2$ and CO at T = 2500 K, we measure a CO/H$_2$ fractional abundance of 2$times$10$^{-3}$, and discuss possible reasons why this value is in excess of the canonical 10$^{-4}$ value, including dust attenuation, incorrect assumptions on co-spatiality of the H$_2$ and CO emission, and chemical processing in an extreme environment. We model the radiative transfer of H$_2$ in this region with UV pumping models to look for signatures of H$_2$ fluorescence from H I Ly$alpha$ pumping. Dissociative (J-type) shocks and nebular emission from the foreground Orion H II region are considered as possible Ly$alpha$ sources. From our radiative transfer models, we predict that signatures of Ly$alpha$ pumping should be detectable in near-IR line ratios given a sufficiently strong source, but such a source is not present in the BN/KL outflow. The data are consistent with shocks as the H$_2$ heating source.
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