The extended ionized gas in Seyfert and Radio-Galaxies is characterized by large values of the ratio He ii/Hβ, which exceeds the value predicted by the standard photoionization model in which the ionizing continuum consists of a power-law. This has lead to the suggestion of considering a matter-bounded (MB) component for explaining such extreme values. We now find that it is also possible to resolve the temperature problem if the thickness and the ionization parameter of the MB is appropriately selected. Adopting a canonical power law (α= −1.3) and solar abundances (Z=l), we can account for the observed trends in excitation (represented for example by the ratio [0 ii]/[0 iii] in Fig. 1)) by varying the relative number of MB clouds (which emit the high excitation lines Civ, [Ne v], He ii… and most of [O iii]) versus the number of ionization-bounded (IB) clouds (which emit [N ii],[S ii] [O ii], [O i]…). We obtain a one-parameter sequence (solid line) which is function of the weight AM/I of the MB component relative to the IB component. This AM/I–sequence successfully reproduces the observed range in He ii/Hβ. Note the failure of the traditional U–sequence (long dashed line). Fig. 2 indicates that we can also reproduce the ratio ROIII= [O III]λ4363/[O iii]λ5007 and therefore resolve the temperature problem. Interestingly, our model indicates a temperature difference of 5 000 K between the IB component ([N ii] temperature ≃ 10 000 K) and the MB component ([O iii] temperature ≃ 15 000 K) while the traditional U–sequence predicts a difference of only 1 000 K. Such difference of 5 000 K has been reported in the extended gas of Cygnus A.