  We report measurements of the electron temperature at about a dozen locations
in the extended emission-line regions of five active (Seyfert and radio)
galaxies. Temperatures (T_{[OIII]} and T_{[NII]}) have been determined from
both the I([OIII]\lambda4363)/I([OIII]\lambda5007) and
I([NII]\lambda5755)/I[NII]\lambda6583) ratios. T_{[OIII]} lies in the range
(1.0 -- 1.7) \times 10^{4}K. We find a strong trend for T_{[OIII]} to be higher
than T_{[NII]}, with the difference typically being \approx 5,000K. Because the
critical density for collisional de-excitation of the ^{1}D{_2} level in NII is
lower than that of the same level in OIII, the deviations of the measured
intensity ratios from those expected for T_{[OIII]} = T_{[NII]} in the low
density limit are unlikely to result from collisional de-excitation. The
measured values of T_{[OIII]} and the differences between T_{[OIII]} and
T_{[NII]} are very similar to those found in Galactic planetary nebulae. It is
argued that the dominant form of energy input to the clouds is photoionization,
but detailed modelling indicates that the temperature difference is too large
to be accounted for in terms of photoionization of ionization-bounded clouds.
We propose instead that both matter- and ionization-bounded clouds are present
in the extended emission-line regions, with most of the [OIII] emission
originating from a hot zone in the matter-bounded clouds and essentially all of
the [NII] from the ionization-bounded clouds.
