  We study the implications of primordial magnetic fields for the thermal and
ionization history of the post-recombination era. In particular we compute the
effects of dissipation of primordial magnetic fields owing to ambipolar
diffusion and decaying turbulence in the intergalactic medium (IGM) and the
collapsing halos and compute the effects of the altered thermal and ionization
history on the formation of molecular hydrogen. We show that, for magnetic
field strengths in the range $2 \times 10^{-10} {\rm G} \la B_0 \la 2 \times
10^{-9} {\rm G}$, the molecular hydrogen fraction in IGM and collapsing halo
can increase by a factor 5 to 1000 over the case with no magnetic fields. We
discuss the implication of the increased molecular hydrogen fraction on the
radiative transfer of UV photons and the formation of first structures in the
universe.
