  Detailed hydrodynamic modeling explained several features of a fragment of
the core of a Coronal Mass Ejection observed with SoHO/UVCS at 1.7 Ro on 12
December 1997, but some questions remained unsolved. We investigate the role of
the magnetic fields in the thermal insulation and the expansion of an ejected
fragment (cloud) traveling upwards in the outer corona. We perform MHD
simulations including the effects of thermal conduction and radiative losses of
a dense spherical or cylindrical cloud launched upwards in the outer corona,
with various assumptions on the strength and topology of the ambient magnetic
field; we also consider the case of a cylindrical cloud with an internal
magnetic field component along its axis. We find that a weak ambient magnetic
field (beta~20) with open topology provides both significant thermal insulation
and large expansion. The cylindrical cloud expands more than the spherical one.
