A photoionized gas in thermal equilibrium can display a thermal instability, with 3 or more solutions in the multi-branch region of the S-shape curve giving the temperature versus the radiation-to-gas-pressure ratio. Many studies have been devoted to this curve and to its dependence on different parameters, always in the optically thin case. The purpose of our study is the thermal instability in optically thick, stratified media, in total pressure equilibrium. We have developped a new algorithm

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... to select the hot/cold stable solution, and thereof to compute a fully consistent photoionization model. We have implemented it in the TITAN code and computed a set of models encompassing the range of conditions valid for the Warm Absorber in Active Galactic Nuclei. We have demonstrated that the thermal instability problem is quite different in thin or thick media. In thick media the spectral distribution changes as the radiation progresses inside the ionized gas. This has observational implications in the emitted/absorbed spectra, ionization states, and variability. However impossible to know what solution the plasma will adopt when attaining the multi-solutions regime, we expect the emitted/absorbed spectrum to be intermediate between those resulting from pure cold and hot models. Large spectral fluctuations corresponding to the onset of a cold/hot solution could be observed in timescales of the order of the dynamical time. A strong turbulence implying supersonic velocities should permanently exist in the multi-branch region of thick, stratified, pressure equilibrium media.