NGC 1097 is a nearby Seyfert 1 galaxy with a bright circumnuclear starburst ring, a strong large-scale bar and an active nucleus. We present a detailed study of the spatial variation of the far infrared (FIR) [CII]158µm and [OI]63µm lines and mid-infrared H_2 emission lines as tracers of gas cooling, and of the polycyclic aromatic hydrocarbon (PAH) bands as tracers of the photoelectric heating, using Herschel-PACS, and Spitzer-IRS infrared spectral maps. We focus on the nucleus and the ring, and two star forming regions (Enuc N and Enuc S). We estimated a photoelectric gas heating efficiency ([CII]158µm+[OI]63µm)/PAH in the ring about 50% lower than in Enuc N and S. The average 11.3/7.7µm PAH ratio is also lower in the ring, which may suggest a larger fraction of ionized PAHs, but no clear correlation with [CII]158µm/PAH(5.5 - 14µm) is found. PAHs in the ring are responsible for a factor of two more [CII]158µm and [OI]63µm emission per unit mass than PAHs in the Enuc S. SED modeling indicates that at most 25% of the FIR power in the ring and Enuc S can come from high intensity photodissociation regions (PDRs), in which case G_0 ~ 10^(2.3) and n_H ~ 10^(3.5) cm^(-3) in the ring. For these values of G_0 and n_H PDR models cannot reproduce the observed H_2 emission. Much of the the H_2 emission in the starburst ring could come from warm regions in the diffuse ISM that are heated by turbulent dissipation or shocks.