  We have measured the thermal conductivity of a TlCuCl$_3$ single crystal in
magnetic fields up to 14 T. It has been found that the temperature dependence
of the thermal conductivity exhibits a sharp peak at 4 K in zero field, which
is suppressed by the application of magnetic fields up to 7 T. The peak is
concluded to be attributable to the enhancement of the thermal conductivity due
to phonons because of the formation of a spin-gap state. In high magnetic
fields above 7 T, on the other hand, another sharp peak appears around 4 K and
this is enhanced with increasing magnetic field. This peak is regarded as being
attributable to the enhancement of the thermal conductivity due to magnons
and/or phonons because of the drastic extension of the mean free path of
magnons and/or phonons in the Bose-Einstein condensed state.
