We report the results of spectroscopic mapping observations carried out toward the Herbig-Haro objects HH7–11 and HH54 over the 5.2 - 37 \mu m region using the Infrared Spectrograph of the Spitzer Space Telescope . These observations have led to the detection and mapping of the S ( 0 ) – S ( 7 ) pure rotational lines of molecular hydrogen , together with emissions in fine structure transitions of Ne ^ { + } , Si ^ { + } , S , and Fe ^ { + } . The H _ { 2 } rotational emissions indicate the presence of warm gas with a mixture of temperatures in the range 400 - 1200 K – consistent with the expected temperature behind nondissociative shocks of velocity \sim 10 - 20 km s ^ { -1 } – while the fine structure emissions originate in faster shocks of velocity \sim 35 - 90 km s ^ { -1 } that are dissociative and ionizing . Maps of the H _ { 2 } line ratios reveal little spatial variation in the typical admixture of gas temperatures in the mapped regions , but show that the H _ { 2 } ortho-to-para ratio is quite variable , typically falling substantially below the equilibrium value of 3 attained at the measured gas temperatures . The non-equilibrium ortho-to-para ratios are characteristic of temperatures as low as \sim 50 K , and are a remnant of an earlier epoch , before the gas temperature was elevated by the passage of a shock . Correlations between the gas temperature and H _ { 2 } ortho-to-para ratio show that ortho-to-para ratios < 0.8 are attained only at gas temperatures below \sim 900 K ; this behavior is consistent with theoretical models in which the conversion of para- to ortho-H _ { 2 } behind the shock is driven by reactive collisions with atomic hydrogen , a process which possesses a substantial activation energy barrier ( E _ { A } / k \sim 4000 K ) and is therefore very inefficient at low temperature . The lowest observed ortho-to-para ratios of only \sim 0.25 suggest that the shocks in HH54 and HH7 are propagating into cold clouds of temperature \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 50 K in which the H _ { 2 } ortho-to-para ratio is close to equilibrium .