  The physical properties of galactic halo gas have a profound impact on the
life cycle of galaxies. As gas travels through a galactic halo, it undergoes
dynamical interactions, influencing its impact on star formation and the
chemical evolution of the galactic disk. In the Milky-Way halo, considerable
effort has been made to understand the spatial distribution of neutral gas,
which are mostly in the form of large complexes. However, the internal
variations of their physical properties remains unclear. In this study, we
investigate the thermal and dynamical state of the neutral gas in HVCs.
High-resolution observations (1.'1) of the 21 cm line emission in the EN field
of the DHIGLS HI survey are used to analyze the physical properties of the
bright concentration C I B located at an edge of complex C. We use the Gaussian
decomposition code ROHSA to model its multiphase content, and perform a power
spectrum analysis to analyze its multi-scale structure. Physical properties of
some 200 structures extracted using dendrograms are examined. We identify two
distinct regions, one of which has a prominent protrusion extending from the
edge of complex C that exhibits an ongoing phase transition from warm diffuse
gas to cold dense gas and filaments. The scale at which the warm gas becomes
unstable and undergoes a thermal condensation is about 15 pc, corresponding to
a cooling time about 1.5 Myr. We find that a transition from subsonic to
trans-sonic turbulence is associated with the thermal condensation. A large
scale perspective of complex C suggests that hydrodynamic instabilities are
involved in creating the structured concentration C I B and the phase
transition therein. However, the details of the dynamical and thermal processes
remain unclear and will require further investigation, through both
observations and numerical simulations. (Shortened for arxiv)
