The excitation of the filamentary gas structures surrounding giant elliptical galaxies at the center of cool-core clusters, a.k.a BCGs (brightest cluster galaxies), is key to our understanding of active galactic nucleus feedback, and of the impact of environmental and local effects on star formation. We investigate the contribution of the thermal radiation from the cooling flow surrounding BCGs to the excitation of the filaments. We explore the effects of small levels of extra-heating (turbulence), and of metallicity, on the optical and infrared lines. Using the Cloudy code, we model the photoionization and photodissociation of a slab of gas of optical depth AV{leq}30mag at constant pressure, in order to calculate self-consistently all of the gas phases, from ionized gas to molecular gas. The ionizing source is the EUV and soft X-ray radiation emitted by the cooling gas. We test these models comparing their predictions to the rich multi-wavelength observations, from optical to submillimeter. These models reproduce most of the multi-wavelength spectra observed in the nebulae surrounding the BCGs, not only the LINER-like optical diagnostics: [O iii]{lambda} 5007 {AA}/Hb{eta}, [N ii]{lambda} 6583 {AA}/H{alpha} and ([S ii]{lambda} 6716 {AA}+[S ii]{lambda} 6731 {AA})/H{alpha} but also the infrared emission lines from the atomic gas. The modeled ro-vib H2 lines also match observations, which indicates that near and mid-IR H2 lines are mostly excited by collisions between H2 molecules and secondary electrons produced naturally inside the cloud by the interaction between the X-rays and the cold gas in the filament. However, there is still some tension between ionized and molecular line tracers (i.e. CO), which requires to optimize the cloud structure and the density of the molecular zone.