  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 Observatory's
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.
