  We present a detailed analysis of the X-ray, infrared, and carbon monoxide
(CO) emission for a sample of 35 local ($z \leq 0.15$), active ($L_X \geq
10^{42}$ erg s$^{-1}$) galaxies. Our goal is to infer the contribution of
far-ultraviolet (FUV) radiation from star formation (SF), and X-ray radiation
from the active galactic nuclei (AGN), respectively producing photodissociation
regions (PDRs) and X-ray dominated regions (XDRs), to the molecular gas
heating. To this aim, we exploit the CO spectral line energy distribution (CO
SLED) as traced by Herschel, complemented with data from single-dish telescopes
for the low-J lines, and high-resolution ALMA images of the mid-J CO emitting
region. By comparing our results to the Schmidt-Kennicutt relation, we find no
evidence for AGN influence on the cold and low-density gas on kpc-scales. On
nuclear (r = 250 pc) scales, we find weak correlations between the CO line
ratios and either the FUV or X-ray fluxes: this may indicate that neither SF
nor AGN radiation dominates the gas excitation, at least at r = 250 pc. From a
comparison of the CO line ratios with PDR and XDR models, we find that PDRs can
reproduce observations only in presence of extremely high gas densities ($n >
10^5$ cm$^{-3}$). In the XDR case, instead, the models suggest moderate
densities ($n \approx 10^{2-4}$ cm$^{-3}$). We conclude that a mix of the two
mechanisms (PDR for the mid-J, XDR or possibly shocks for the high-J) is
necessary to explain the observed CO excitation in active galaxies.
