  Galaxy clusters host a large reservoir of diffuse plasma with
radially-varying temperature profiles. The efficiency of thermal conduction in
the intracluster medium (ICM) is complicated by the existence of turbulence and
magnetic fields, and has received a lot of attention in the literature.
Previous studies suggest that the magnetothermal instability developed in outer
regions of galaxy clusters would drive magnetic field lines preferentially
radial, resulting in efficient conduction along the radial direction. Using a
series of spherically-symmetric simulations, here we investigate the impact of
thermal conduction on the observed temperature distributions in outer regions
of three massive clusters, and find that thermal conduction substantially
modifies the ICM temperature profile. Within 3 Gyr, the gas temperature at a
representative radius of $0.3r_{500}$ typically decreases by ~10 - 20% and the
average temperature slope between $0.3r_{500}$ and $r_{500}$ drops by ~ 30 -
40%, indicating that the observed ICM would not stay in a long-term equilibrium
state in the presence of thermal conduction. However, X-ray observations show
that the outer regions of massive clusters have remarkably similar
radially-declining temperature profiles, suggesting that they should be quite
stable. Our study thus suggests that the effective conductivity along the
radial direction must be suppressed below the Spitzer value by a factor of 10
or more, unless additional heating sources offset conductive cooling and
maintain the observed temperature distributions. Our study provides a
smoking-gun evidence for the suppression of parallel conduction along magnetic
field lines in low-collisionality plasmas by kinetic mirror or whistler
instabilities.
