  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), CO(1-0), and CO(7-6) emission lines with the APEX 12-m and NRO 45-m
telescopes. We complemented these single-dish observations with CO(1-0),
CO(3-2), and CO(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 CO(1-0) in
literature, showing that part of the gas in this system is CO-poor. Additional
spatially resolved CI observations in both transitions, CO(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.
