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)
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