We present a detailed analysis of the X-ray and molecular gas emission in the nearby galaxy NGC 34 , to constrain the properties of molecular gas , and assess whether , and to what extent , the radiation produced by the accretion onto the central black hole affects the CO line emission . We analyse the CO Spectral Line Energy Distribution ( SLED ) as resulting mainly from Herschel and ALMA data , along with X-ray data from NuSTAR and XMM- Newton . The X-ray data analysis suggests the presence of a heavily obscured AGN with an intrinsic luminosity of L _ { 1 - 100 keV } \simeq 4.0 \times 10 ^ { 42 } erg s ^ { -1 } . ALMA high resolution data ( \theta \simeq 0.2 ^ { \prime \prime } ) allows us to scan the nuclear region down to a spatial scale of \approx 100 pc for the CO ( 6–5 ) transition . We model the observed SLED using Photo-Dissociation Region ( PDR ) , X-ray-Dominated Region ( XDR ) , and shock models , finding that a combination of a PDR and an XDR provides the best fit to the observations . The PDR component , characterized by gas density { log } ( n / { cm ^ { -3 } } ) = 2.5 and temperature T = 30 K , reproduces the low-J CO line luminosities . The XDR is instead characterised by a denser and warmer gas ( { log } ( n / { cm ^ { -3 } } ) = 4.5 , T = 65 K ) , and is necessary to fit the high-J transitions . The addition of a third component to account for the presence of shocks has been also tested but does not improve the fit of the CO SLED . We conclude that the AGN contribution is significant in heating the molecular gas in NGC 34 .