  We observed an enhancement of the $c$-axis differential conductance around
the zero-bias in Au$/$Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212) junctions near the
superconducting transition temperature $T_c$. We attribute the conductance
enhancement to the Andreev reflection between the surface Cu-O bilayer with
suppressed superconductivity and the neighboring superconducting inner bilayer.
The continuous evolution from depression to an enhancement of the zero-bias
differential conductance, as the temperature approaches $T_c$ from below,
points to weakening of the barrier strength of the non-superconducting layer
between adjacent Cu-O bilayers. We observed that the conductance enhancement
persisted up to a few degrees above $T_c$ in junctions prepared on slightly
overdoped Bi2212 crystals. However, no conductance enhancement was observed
above $T_c$ in underdoped crystals, although recently proposed theoretical
consideration suggests an even wider temperature range of enhanced zero-bias
conductance. This seems to provide negative perspective to the existence of the
phase-incoherent preformed pairs in the pseudogap state.
