  We analyze the transformation from insulator to metal induced by thermal
fluctuations within the Falicov-Kimball model. Using the Dynamic Mean Field
Theory (DMFT) formalism on the Bethe lattice we find rigorously the temperature
dependent Density of States ($DOS$) at half filling in the limit of high
dimensions. At zero temperature (T=0) the system is ordered to form the
checkerboard pattern and the $DOS$ has the gap $\Delta$ at the Fermi level
$\varepsilon_F=0$, which is proportional to the interaction constant $U$. With
an increase of $T$ the $DOS$ evolves in various ways that depend on $U$. For
$U>U_{cr}$ the gap persists for any $T$ (then $\Delta >0$), so the system is
always an insulator. However, if $U < U_{cr}$, two additional subbands develop
inside the gap. They become wider with increasing $T$ and at a certain
$U$-dependent temperature $T_{MI}$ they join with each other at
$\varepsilon_F$. Since above $T_{MI}$ the $DOS$ is positive at $\varepsilon_F$,
we interpret $T_{MI}$ as the transformation temperature from insulator to
metal. It appears, that $T_{MI}$ approaches the order-disorder phase transition
temperature $T_{O-DO}$ when $U$ is close to 0 or $ U_{cr}$, but $T_{MI}$ is
substantially lower than $T_{O-DO}$ for intermediate values of $U$. Having
calculated the temperature dependent $DOS$ we study thermodynamic properties of
the system starting from its free energy $F$. Then we find how the order
parameter $d$ and the gap $\Delta $ change with $T$ and we construct the phase
diagram in the variables $T$ and $U$, where we display regions of stability of
four different phases: ordered insulator, ordered metal, disordered insulator
and disordered metal. Finally, we use a low temperature expansion to
demonstrate the existence of a nonzero DOS at a characteristic value of U on a
general bipartite lattice.
