  We present a high-resolution (R=140,000) spectrum of the bright quasar
HE0001-2340 (z=2.26), obtained with ESPRESSO at the Very Large Telescope. We
analyse three systems at z=0.45, z=1.65, and z=2.19 using multiple-component
Voigt-profile fitting. We also compare our spectrum with those obtained with
VLT/UVES, covering a total period of 17 years. We disentangle turbulent and
thermal broadening in many components spread over about 400 km/s in the z~2.19
sub-DLA system. We derive an average temperature of 16000+/-1300 K, i.e., about
twice the canonical value of the warm neutral medium in the Galactic
interstellar medium. A comparison with other high-z, low-metallicity absorbers
reveals an anti-correlation between gas temperature and total HI column
density. Although requiring confirmation, this could be the first observational
evidence of a thermal decrease with galacto-centric distance, i.e., we may be
witnessing a thermal transition between the circum-galactic medium and the
cooler ISM. We revisit the Mg isotopic ratios at z=0.45 and z=1.65 and
constrain them to be xi = (26Mg+25Mg)/24Mg <0.6 and <1.4 in these two systems,
respectively. These values are consistent with the standard Solar ratio, i.e.,
we do not confirm strong enhancement of heavy isotopes previously inferred from
UVES data. Finally, we confirm the partial coverage of the quasar emission-line
region by a FeI-bearing cloud in the z=0.45 system and present evidence for
velocity sub-structure of the gas that has Doppler parameters of the order of
only ~0.3 km/s. This work demonstrates the uniqueness of high-fidelity,
high-resolution optical spectrographs on large telescopes as tools to
investigate the thermal state of the gas in and around galaxies as well as its
spatial and velocity structure on small scales, and to constrain the associated
stellar nucleosynthetic history. [abridged]
