  One of the most important factors in determining the stellar lithium
abundance is the effective temperature. In a previous study by the authors, new
effective temperatures Teff for sixteen metal-poor halo dwarfs were derived
using a local thermodynamic equilibrium (LTE) description of the formation of
Fe lines. This new Teff scale reinforced the discrepancy. For six of the stars
from our previous study we calculate revised temperatures using a non-local
thermodynamic equilibrium (NLTE) approach. These are then used to derive a new
mean primordial lithium abundance in an attempt to solve the lithium
discrepancy. Using the code MULTI we calculate NLTE corrections to the LTE
abundances for the Fe I lines measured in the six stars, and determine new
Teff's. We keep other physical parameters, i.e. log g, [Fe/H] and xi, constant
at the values calculated in Paper I. With the revised Teff scale we derive new
Li abundances. We compare the NLTE values of Teff with the photometric
temperatures of Ryan et al. (1999, ApJ, 523, 654), the infrared flux method
(IRFM) temperatures of Melendez & Ramirez (2004, ApJ, 615, 33), and the Balmer
line wing temperatures of Asplund et al. (2006, ApJ, 644, 229). We find that
our temperatures are hotter than both the Ryan et al. and Asplund et al.
temperatures by typically ~ 110 K - 160 K, but are still cooler than the
temperatures of Melendez & Ramirez by typically ~ 190 K. The temperatures imply
a primordial Li abundance of 2.19 dex or 2.21 dex, depending on the magnitude
of collisions with hydrogen in the calculations, still well below the value of
2.72 dex inferred from WMAP + BBN. We discuss the effects of collisions on
trends of 7Li abundances with [Fe/H] and Teff, as well as the NLTE effects on
the determination of log g through ionization equilibrium, which imply a
collisional scaling factor SH > 1 for collisions between Fe and H atoms.
