We measure H_2 temperatures and column densities across the Orion Becklin-Neugebauer/Kleinmann-Low (BN/KL) explosive outflow from a set of 13 near-infrared (IR) H_2 rovibrational emission lines observed with the TripleSpec spectrograph on Apache Point Observatory's 3.5 m 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 H2 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/H2 fractional abundance of 2 × 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 ultraviolet (UV) pumping models to look for signatures of H_2 fluorescence from H i Lyα pumping. Dissociative (J-type) shocks and nebular emission from the foreground Orion H ii region are considered as possible Lyα sources. From our radiative transfer models, we predict that signatures of Lyα 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