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We present a systematic investigation of X-ray thermal coronae in 157early-type galaxies and 22 late-type galaxies from a survey of 25 hot (kT>3keV), nearby (z<0.05) clusters, based on CHANDRA archival data. Cool galacticcoronae (kT=0.5-1.1 keV generally) have been found to be very common, >60% inNIR selected galaxies that are more luminous than 2L*, and >40% in L* < L_Ks <2L* galaxies. These embedded coronae in hot clusters are generally smaller(1.5-4 kpc radii), less luminous (<~ 10^41 erg s^-1), and less massive(10^6.5-10^8 M_solar}) than coronae in poor environments, demonstrating thenegative effects of hot cluster environments on galactic coronae. Nevertheless,these coronae still manage to survive ICM stripping, evaporation, rapidcooling, and powerful AGN outflows, making them a rich source of informationabout gas stripping, microscopic transport, and feedback processes in thecluster environment. Heat conduction across the boundary of the coronae has tobe suppressed by a factor of >100, which implies the X-ray gas in early-typegalaxies is magnetized and the magnetic field plays an important role in energytransfer. Stripping through transport processes (viscosity or turbulence) alsoneeds to be suppressed by at least a factor of ten at the coronal boundary...(abridged) Diffuse thermal coronae have also been detected in at least 8 of 22late-type (Sb or later) galaxies in our sample. Evidence for enhanced starformation triggered by the ICM pressure has been found in four late-typegalaxies. The fraction of luminous X-ray AGN (>10^41 ergs s^-1) is not small (~5%) in our sample.

X‐Ray Thermal Coronae of Galaxies in Hot Clusters: Ubiquity of Embedded Mini–Cooling Cores