  We compute the anisotropic electrical conductivity tensor of the inner crust
of a compact star at non-zero temperature by extending a previous work on the
conductivity of the outer crust. The physical scenarios, where such crust is
formed, involve proto-neutron stars born in supernova explosions, binary
neutron star mergers and accreting neutron stars. The temperature-density range
studied covers the transition from a non-degenerate to a highly degenerate
electron gas and assumes that the nuclei form a liquid, i.e., the temperature
is above the melting temperature of the lattice of nuclei. The electronic
transition probabilities include (a) the dynamical screening of electron-ion
interaction in the hard-thermal-loop approximation for the QED plasma, (b) the
correlations of the ionic component in a one-component plasma, and (c) finite
nuclear size effects. The conductivity tensor is obtained from the Boltzmann
kinetic equation in relaxation time approximation accounting for the
anisotropies introduced by a magnetic field. The sensitivity of the results
towards the matter composition of the inner crust is explored by using several
compositions of the inner crust which were obtained using different nuclear
interactions and methods of solving the many-body problem. The standard
deviation of relaxation time and components of the conductivity tensor from the
average are below $\le 10\%$ except close to crust-core transition, where
non-spherical nuclear structures are expected. Our results can be used in
dissipative magneto-hydrodynamics (MHD) simulations of warm compact stars.
