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We examine the processes expected to be important in pressurizing the ISM atomic H~I phase, determine the significance of each, and ascertain whether the problem of maintaining the observed H~I pressure regime is well constrained. The heating processes considered here are: cosmic--ray heating, X--Ray Auger processes, photoelectic heating from ``classical'' grains and small organic grains, and contributions from Polycyclic Aromatic Hydrocarbon (PAH) molecules. The cooling is computed from collisional excitation by electrons, hydrogen atoms, and protons in multiple-level atom models. Recombination heating and grain collisional cooling are also included. Recent laboratory PAH data, up-to-date atomic data, and detailed process models are used. With the large uncertainties in our knowlege of the small grain properties, it remains unclear whether the PAHs are indeed the main source of photoelectric heating. Models based on a reasonable (and conservative) extended-MRN distribution of small organic grains down to 10~\AA\ are able to produce pressures in the range of the observations without the need to introduce PAH molecules at all. If PAHs are included, then upper limits on their abundances can possibly be obtained.
