  We present VLT-UVES Li abundances for 28 halo dwarf stars between [Fe/H]=-2.5
and -3.5, 10 of which have [Fe/H]<-3. Four different T_eff scales have been
used. Direct Infrared Flux Method (IRFM) has been used on the basis of 2MASS
infrared photometry. H_alpha wings have been fitted against synthetic grids
computed by means of 1D LTE atmosphere models, assuming different
self-broadening theories. Finally, a grid of H_alpha profiles has been computed
by means of 3D hydrodynamical atmosphere models. The Li I doublet at 670.8 nm
has been used to measure A(Li) by means of 3D hydrodynamical NLTE spectral
syntheses. An analytical fit of A(Li)(3D, NLTE) as a function of equivalent
width, T_eff, log g, and [Fe/H] has been derived and is made available. A(Li)
does not exhibit a plateau below [Fe/H]=-3. A strong positive correlation with
[Fe/H] appears, not influenced by the choice of the T_eff estimator. From a
linear fit, we obtain a strong slope of about 0.30 dex in A(Li) per dex in
[Fe/H], significant to 2-3 sigma, and consistent among all the four T_eff
estimators. A significant slope is also detected in the A(Li)--T_eff plane,
driven mainly by the coolest stars in the sample which appear Li-poor. Removing
such stars does not alter the behavior in the A(Li)-[Fe/H] plane. The scatter
in A(Li) increases by a factor of 2 towards lower metallicities, while the
plateau appears very thin above [Fe/H]=-2.8. The meltdown of the Spite plateau
below [Fe/H]\sim-3 is established, but its cause is unclear. If the primordial
A(Li) is the one derived from WMAP, it appears difficult to envision a single
depletion phenomenon producing a thin, metallicity independent plateau above
[Fe/H]=-2.8, and a highly scattered, metallicity dependent distribution below.
The fact that no star below [Fe/H]=-3 lies above the plateau suggests that they
formed at plateau level and underwent subsequent depletion.
