  The effective temperature (Teff) of the radiation field of the ionizing
star(s) of a large sample of extragalactic HII regions was estimated using the
R= log([OII](3727)/[OIII]5007) index. We used a grid of photoionization models
to calibrate the Teff-R relation finding that it has a strong dependence with
the ionizing parameter while it shows a weak direct dependence with the
metallicity (variations in Z imply variations in U) of both the stellar
atmosphere of the ionizing star and the gas phase of the HII region. Since the
R index varies slightly with the Teff for values larger than 40 kK, the R index
can be used to derive the Teff in 30-40 kK range. A large fraction of the
ionization parameter variation is due to differences in the temperature of the
ionizing stars and then the use of the (relatively) low Teff dependent S2=[S
II](6717+31)/Ha emission-line ratio to derive the ionization parameter is
preferable over others in the literature. We propose linear metallicity
dependent relationships between S2 and U. Teff and metallicity estimations for
a sample of 865 HII regions, whose emission-line intensities were compiled from
the literature, do not show any Teff-Z correlation. On the other hand it seems
to be hints of the presence of an anti-correlation between Teff-U. We found
that the majority of the studied HII regions (87%) present Teff values in the
range between 37 and 40 kK, with an average value of 38.5 kK. We also studied
the variation of Teff as a function of the galactocentric distance for 14
spiral galaxies. Our results are in agreement with the idea of the existence of
positive Teff gradients along the disk of spiral galaxies.
