  We analyse 2,015 mid-infrared (MIR) spectra of galaxies observed with
Spitzer's Infrared Spectrograph, including objects with growing super-massive
black holes and objects where most of the infrared emission originates from
newly formed stars. We determine if and how accreting super-massive black holes
at the centre of galaxies -- known as active galactic nuclei (AGN) -- heat and
ionize their host galaxies' dust and molecular gas. We use four MIR diagnostics
to estimate the contribution of the AGN to the total MIR emission. We refer to
galaxies whose AGN contribute more than 50 per cent of the total MIR emission
as AGN-dominated. We compare the relative strengths of PAH emission features
and find that PAH grains in AGN-dominated sources have a wider range of sizes
and fractional ionizations than PAH grains in non-AGN dominated sources. We
measure rotational transitions of H_2 and estimate H_2 excitation temperatures
and masses for individual targets, H_2 excitation temperatures for spectra
stacked by their AGN contribution to the MIR, and the H_2 excitation
temperature distributions via a hierarchical Bayesian model. We find an average
200 K difference between the excitation temperatures of the H_2 S(5) and H_2
S(7) pure rotational molecular hydrogen transition pair in AGN-dominated versus
non-AGN dominated galaxies. Our findings suggest that AGN impact the
interstellar medium of their host galaxies.
