We present measurements of 5-25 {mu}m emission features of brightest cluster galaxies (BCGs) with strong optical emission lines in a sample of 9 cool-core clusters of galaxies observed with the Infrared Spectrograph on board the Spitzer Space Telescope. These systems provide a view of dusty molecular gas and star formation, surrounded by dense, X-ray emitting intracluster gas. Past work has shown that BCGs in cool-core clusters may host powerful radio sources, luminous optical emission line systems, and excess UV, while BCGs in other clusters never show this activity. In this sample, we detect polycyclic aromatic hydrocarbons (PAHs), extremely luminous, rotationally-excited molecular hydrogen line emission, forbidden line emission from ionized gas ([Ne II] and [Ne III]), and infrared continuum emission from warm dust and cool stars. We show here that these BCGs exhibit more luminous forbidden neon and H2 rotational line emission than star-forming galaxies with similar total infrared luminosities, as well as somewhat higher ratios of 70 {mu}m / 24 {mu}m luminosities. Our analysis suggests that while star formation processes dominate the heating of the dust and PAHs, a heating process consistent with suprathermal electron heating from the hot gas, distinct from star formation, is heating the molecular gas and contributing to the heating of the ionized gas in the galaxies. The survival of PAHs and dust suggests that dusty gas is somehow shielded from significant interaction with the X-ray gas.