  We calculate the evolution of Li6 generated from cosmic rays produced by an
early population of massive stars. The computation is performed in the
framework of hierarchical structure formation and is based on cosmic star
formation histories constrained to reproduce the observed star formation rate
at redshift z \la 6, the observed chemical abundances in damped Lyman alpha
absorbers and in the intergalactic medium, and to allow for an early
reionization of the Universe at z\sim 11 by Pop III stars as indicated by the
third year results released by WMAP. We show that the pregalactic production of
the Li6 isotope in the IGM via these Pop III stars can account for the Li6
plateau observed in metal poor halo stars without additional over-production of
Li7. Our results depend on the efficiency of cosmic rays to propagate out of
minihalos and the fraction of supernovae energy deposited in cosmic rays. We
also compute the cosmic ray heating of the IGM gas. In general, we find
somewhat high temperatures (of order 10^5 K) implying that the cosmic rays
production of Li6 may be required to be confined to the so-called warm-hot IGM.
