We searched for 21-cm absorption associated with the z_abs = 1.3647
absorption system toward PKS 0237-233 using the GMRT. A high quality UVES
spectrum shows that C I and C I* are detected at this redshift together with C
II*, Mg I, Mg II, Si II, Al II, Fe II and Mn II. The complex profiles, spread
over ~300 km/s, are fitted with 21 Voigt profile components. None of these
components are detected in 21-cm absorption down to a detection limit of
\tau(3\sigma)\le 3x10^{-3} (or N(HI)/T_S <10^{17} cm ^-2 K^-1). We derive log
N(HI)<19.30±0.30 using the Lyman alpha absorption line detected in the IUE
spectrum of the quasar. Mg II, Si II and Al II column densities are consistent
with near solar metallicity and we measure [O/H]>-0.33. Using photoionization
models constrained by the fine-structure excitations of C I and C II, and the
21-cm optical depth, we show that the C I absorption arises predominantly
either in WIM or WNM in ionization and thermal equilibrium with the
meta-galactic UV background dominated by QSOs and star forming galaxies. The
estimated thermal pressure of the gas is of the same order of magnitude over
different velocity ranges through the absorption profile (2.6\le log [P/k
cm^{-3} K]\le 4.0). The gas-phase metallicity corrected for ionization is Z>0.5
Z_\odot with a signature of Fe co-production elements being under abundant
compared to \alpha-process elements by ~0.5 dex. At z>1.9, C I absorption is
usually associated with H_2 absorption arising from cold gas in DLAs. This
system and the z=2.139 toward Tol 1037-270 are the only two systems known which
show that C I absorption can also be detected in warm gas provided the
metallicity is high enough. Interestingly, both the systems are part of unusual
concentrations of absorption lines.Comment: 12 pages, 9 figures, accepted for publication in MNRA