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 on to 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 active galactic nucleus (AGN) with an intrinsic luminosity of L1-100 (keV) similar or equal to 4.0 x 10(42) erg s(-1). ALMA high-resolution data (theta similar or equal to 0.2 arcsec) allow us to scan the nuclear region down to a spatial scale of approximate to 100 pc for the CO(6-5) transition. We model the observed SLED using photodissociation 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 characterized 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.