  The physical state of interstellar gas and dust is dependent on the processes
which heat and cool this medium. To probe heating and cooling of the ISM over a
large range of infrared surface brightness, on sub-kiloparsec scales, we employ
line maps of [C \ii] 158 $\mu$m, [O \one] 63 $\mu$m, and [N \ii] 122 $\mu$m in
NGC 1097 and NGC 4559, obtained with the PACS spectrometer onboard {\it
Herschel}. We matched new observations to existing Spitzer-IRS data that trace
the total emission of polycyclic aromatic hydrocarbons (PAHs). We confirm at
small scales in these galaxies that the canonical measure of photoelectric
heating efficiency, ([C \ii] + [O \one])/TIR, decreases as the far-infrared
color, $\nu f_\nu$(70 $\mu$m)/$\nu f_\nu$(100 $\mu$m), increases. In contrast,
the ratio of far-infrared (far-IR) cooling to total PAH emission, ([C \ii] + [O
\one])/PAH, is a near constant $\sim$6% over a wide range of far-infrared
color, 0.5 \textless\ $\nu f_\nu$(70 $\mu$m)/$\nu f_\nu$(100 $\mu$m) $\lesssim$
0.95. In the warmest regions, where $\nu f_\nu$(70 $\mu$m)/$\nu f_\nu$(100
$\mu$m) $\gtrsim$ 0.95, the ratio ([C \ii] + [O \one])/PAH drops rapidly to 4%.
We derived representative values of the local UV radiation density, $G_0$, and
the gas density, $n_H$, by comparing our observations to models of
photodissociation regions. The ratio $G_0/n_H$, derived from fine-structure
lines, is found to correlate with the mean dust-weighted starlight intensity,
$<U>$ derived from models of the IR SED. Emission from regions that exhibit a
line deficit is characterized by an intense radiation field, indicating that
small grains are susceptible to ionization effects. We note that there is a
shift in the 7.7 / 11.3 $\mu$m PAH ratio in regions that exhibit a deficit in
([C \ii] + [O \one])/PAH, suggesting that small grains are ionized in these
environments.
