The evolution of galaxies is largely affected by exchanging material with their close environment, the circumgalactic medium (CGM). In this work, we investigate the CGM and the interstellar medium (ISM) of the bright central galaxy (BCG) of the galaxy cluster, MACS1931−26 at z ∼ 0.35. We detected [CI](2−1), 12CO(1−0), and 12CO(7−6) emission lines with the APEX 12-m and NRO 45-m telescopes. We complemented these single-dish observations with 12CO(1−0), 12CO(3−2), and 12CO(4−3) ALMA interferometric data and inferred the cold molecular hydrogen physical properties. Using a modified large velocity gradient (LVG) model, we modelled the CO and CI emission of the CGM and BCG to extract the gas thermodynamical properties, including the kinetic temperature, the density, and the virialisation factor. Our study shows that the gas in the BCG is highly excited, comparable to the gas in local ultra luminous infrared galaxies (ULIRGs), while the CGM is likely less excited, colder, less dense, and less bound compared to the ISM of the BCG. The molecular hydrogen mass of the whole system derived using [CI](2−1) is larger than the mass derived from 12CO(1−0) in literature, showing that part of the gas in this system is CO-poor. Additional spatially resolved CI observations in both transitions, [CI](1−0) and [CI](2−1), and the completion of the CO SLED with higher CO transitions are crucial to trace the different phases of the gas in such systems and constrain their properties.