We have mapped the warm molecular gas traced by the H_2 S(0) - H_2 S(5) pure rotational mid-infrared emission lines over a radial strip across the nucleus and disk of M51 (NGC 5194) using the Infrared Spectrograph (IRS) on the Spitzer Space Telescope
. The six H_2 lines have markedly different emission distributions. We obtained the H_2 temperature and surface density distributions by assuming a two temperature model: a warm (T = 100 - 300 K) phase traced by the low J (S(0) - S(2)) lines and a hot phase (T = 400 - 1000 K) traced by the high J (S(2) - S(5)) lines. The lowest molecular gas temperatures are found within the spiral arms (T ~ 155 K), while the highest temperatures are found in the inter-arm regions (T > 700 K). The warm gas surface density reaches a maximum of 11 M_sun/pc^2 in the northwestern spiral arm, whereas the hot gas surface density peaks at 0.24 M_sun/pc^2 at the nucleus. The spatial offset between the peaks in the warm and hot phases and the differences in the distributions of the H_2 line emission suggest that the warm phase is mostly produced by UV photons in star forming regions while the hot phase is mostly produced by shocks or X-rays associated with nuclear activity. The warm H_2 is found in the dust lanes of M51, spatially offset from the brightest HII regions. The warm H_2 is generally spatially coincident with the cold molecular gas traced by CO (J = 1 - 0) emission, consistent with excitation of the warm phase in dense photodissociation regions (PDRs). In contrast, the hot H_2 is most prominent in the nuclear region. Here, over a 0.5 kpc radius around the nucleus of M51, the hot H_2 coincides with [O IV](25.89 micron) and X-ray emission indicating that shocks and/or X-rays are responsible for exciting this phase.
