  In this paper, we use the Mappings photoionization code to explore the
physical parameters that impact on the measurement of electron temperature and
abundance in HII regions. In the previous paper we presented observations and
measurements of physical properties from the spectra of seventeen HII regions
in fourteen isolated dwarf irregular galaxies from the SIGRID sample. Here, we
analyze these observations further, together with three additional published
data sets. We explore the effects of optical thickness, electron density,
ionization parameter, ionization source, and non-equilibrium effects on the
relation between electron temperature and metallicity. We present a standard
model that fits the observed data remarkably well at metallicities between 1/10
and 1 solar. We investigate the effects of optically thin HII regions, and show
that they can have a considerable effect on the measured electron temperature,
and that there is evidence that some of the observed objects are optically
thin. We look at the role of the ionization parameter and find that lower
ionization parameter values give better fits at higher oxygen abundance. We
show that higher pressures combined with low optical depth, and also kappa
electron energy distributions at low kappa values, can generate the apparent
high electron temperatures in low metallicity HII regions, and that the former
provides the better fit to observations. We examine the effects of these
parameters on the strong line diagnostic methods. We extend this to
three-dimensional diagnostic grids to confirm how well the observations are
described by the grids.
