  We investigate the effect of conductive heating of the gas surrounding a
geometrically thick accretion disk on the growth of a black hole at high
redshift. If a black hole is accreting the surrounding gas at a super-Eddington
rate, the X-ray radiation from the vicinity of the black hole would be highly
anisotropic due to the self-shielding of a geometrically thick accretion disk,
and then the radiative feedback on the surrounding medium would be suppressed
in the equatorial region, within which super-Eddington accretion can continue.
However, if this region is sufficiently heated via thermal conduction from the
adjacent region that is not shielded and heated by the X-ray irradiation, the
surrounding gas becomes isotropically hot and the Bondi accretion rate would be
suppressed and become sub-Eddington. We evaluate the condition under which such
isotropic heating is realized, and derive new criteria required for
super-Eddington accretion.
