  We explore the importance of magnetic-field-oriented thermal conduction in
the interaction of supernova remnant (SNR) shocks with radiative gas clouds and
in determining the mass and energy exchange between the clouds and the hot
surrounding medium. We perform 2.5D MHD simulations of a shock impacting on an
isolated gas cloud, including anisotropic thermal conduction and radiative
cooling; we consider the representative case of a Mach 50 shock impacting on a
cloud ten-fold denser than the ambient medium. We consider different
configurations of the ambient magnetic field and compare MHD models with or
without the thermal conduction. The efficiency of the thermal conduction in the
presence of magnetic field is, in general, reduced with respect to the
unmagnetized case. The reduction factor strongly depends on the initial
magnetic field orientation, and it is minimum when the magnetic field is
initially aligned with the direction of shock propagation. The thermal
conduction contributes to suppress hydrodynamic instabilities, reducing the
mass mixing of the cloud and preserving the cloud from complete fragmentation.
Depending on the magnetic field orientation, the heat conduction may determine
a significant energy exchange between the cloud and the hot surrounding medium
which, while remaining always at levels less than those in the unmagnetized
case, leads to a progressive heating and evaporation of the cloud. This
additional heating may contrast the radiative cooling of some parts of the
cloud, preventing the onset of thermal instabilities.
