  In the present work we study the effects of strongly quantizing magnetic
fields and finite temperature on the properties of inner crusts of hot neutron
stars. The inner crust of a neutron star contains neutron-rich nuclei arranged
in a lattice and embedded in gases of free neutrons and electrons. We describe
the system within the Wigner-Seitz (WS) cell approximation. The nuclear energy
is calculated using Skyrme model with SkM* interaction. To isolate the
properties of nuclei we follow the subtraction procedure presented by Bonche,
Levit and Vautherin, within the Thomas-Fermi approximation. We obtain the
equilibrium properties of inner crust for various density, temperatures and
magnetic fields by minimizing the free energy of the WS cell satisfying the
charge neutrality and $\beta-$equilibrium conditions. We infer that at a fixed
baryon density and temperature, strong quantizing magnetic field reduces the
cell radii, neutron and proton numbers in the cell compared with the field free
case. However, the nucleon number in the nucleus increases in presence of
magnetic field. The free energy per nucleon also decreases in magnetized inner
crust. On the other hand, we find that finite temperature tends to smear out
the effects of magnetic field. Our results can be important in the context of
$r-$process nucleosynthesis in the binary neutron star mergers.
