  We study effects of the fully ionized initial state, or pre-ionization, on
the subsequent thermal evolution of low-metallicity clouds under various
intensities of the external far-ultraviolet(FUV) and cosmic-ray(CR) fields. The
pre-ionization significantly affects the thermal and dynamical evolution of
metal-free clouds without FUV/CRs by way of efficient HD formation. On the
other hand, the pre-ionization effect on the thermal evolution is limited in
very low-density regime for more metal-enriched clouds ([Z/H] >~ -4) or those
under modest FUV (>10^{-3}) or CR field (>0.1 of the present-day Galactic disk
levels). In any case, for >10^8 cm^{-3}, neither the initial ionization state
nor the irradiating FUV strength affect the thermal evolution. The dust cooling
is an important mechanism for making sub-solar mass fragments in
low-metallicity gas. Since this fragmentation occurs at the temperature minimum
by the dust cooling at >10^{10} cm^{-3}, this process is not vulnerable either
to initial ionization state or external radiation.
