Аннотация:The thermal equilibrium of Seyfert-nucleus and quasar emission-line clouds that are optically thick in the Lyman continuum is discussed, extending previous results. With optical depth much greater than unity, the gas will be heated through photoionization of helium by the hard-UV and X radiation of the nucleus. The cooling processes include free-free emission in the field of H and He ions, H and He recombination emission, and energy losses to collisional excitation and ionization of H atoms. The effect of 1549 A C IV resonance-line emission on the clouds' thermal balance is estimated. At electron temperatures greater than about 15,000 K, thermal equilibrium will be achieved when the optical depth of a cloud is large enough for the gas to be almost fully thermalized, as indicated also by analysis of relative hydrogen-line intensities. The thermal-balance equation is solved to yield a typical emission-cloud size in good accord with that derived from the hydrogen-line variations.