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We analyze the resolved neutral hydrogen emission properties of a sample ofeleven of the nearest spiral galaxies. Between 60 and 90% of the total HI lineflux within the optical disk is due to a high brightness network (HBN) ofemission features which are marginally resolved in their narrow dimension atabout 150 pc and have a face-on covering factor of about 15%. Averaged lineprofiles of this component are systematically non-Gaussian with a narrow core(less than about 6 km/s FWHM) superposed on broad Lorentzian wings (30 km/sFWHM). An upper limit to the gas temperature of 300 K follows directly from thenarrow line profiles, while simple modeling suggests kinetic temperatures equalto the peak emission brightness temperature (80-200 K) in all cases but theouter disks of low mass galaxies, where the HBN becomes optically thin to the21 cm line. Positive radial gradients in the derived kinetic temperature arefound in all spiral galaxies. The distributions of brightness temperature withradius in our sample form a nested system with galaxies of earliermorphological type systematically displaced to lower temperature at all radii.The fractional line flux due to the HBN plummets abruptly near the edge of theoptical disk where a diffuse outer gas disk takes over. We identify the HBNwith the Cool Neutral Medium.Comment: 22 page LaTeX requires aastex, 10 PS figures. Accepted for  publication in the Ap

The Temperature and Opacity of Atomic Hydrogen in Spiral Galaxies