  The ionization mechanism of the low-ionization gas in quiescent red sequence
galaxies has been a long-standing puzzle. Direct temperature measurements would
put strong constraints on this issue. We carefully selected a sample of
quiescent red sequence galaxies from SDSS. We bin them into three bins with
different [N II]/H{\alpha} and [N II]/[O II] ratios, and we measure the
temperature-sensitive [O III] {\lambda}4363, [N II] {\lambda}5755, [S II]
{\lambda}{\lambda}4068,4076, and [O II] {\lambda}{\lambda}7320,7330 lines in
the stacked spectra. The [S II] doublet ratios indicate the line-emitting gas
is in the low density regime (~10-100 cm$^{-3}$).We found the temperatures in
the S+ zones to be around 8000K, the temperatures in the O+ zones to be around
$1.1-1.5\times10^4$K, and the temperatures in the N+ zones to be around
$1-1.4\times10^4$K. The [O III] {\lambda}4363 line is not robustly detected. We
found that the extinction corrections derived from Balmer decrements would
yield unphysical relationships between the temperatures of the S+ zones and O+
zones, indicating that the extinction is significantly overestimated by the
measured Balmer decrements. We compared these line ratios with model
predictions for three ionization mechanisms: photoionization by hot evolved
stars, shocks, and turbulent mixing layers. For both the photoionization and
shock models, the hot temperatures inferred from [S II] and [N II]
coronal-to-strong line ratios require metallicities to be significantly
subsolar. However, the [N II]/[O II] line ratios require them to be supersolar.
None of the models could simultaneously explain all of the observed line
ratios, neither could their combinations do.
