  The thermal conductivity \kappa of Cu_1-xMg_xGeO_3 is measured in magnetic
fields up to 16 T. At the transition field H_c to the high-field incommensurate
(I) phase, \kappa abruptly decreases. While \kappa of the pure CuGeO_3 is
enhanced with the application of higher magnetic fields, an anomalous plateau
feature shows up in the \kappa(H) profile in the I phase of the Mg-doped
samples which includes antiferromagnetic ordering (I-AF phase). With the help
of specific heat data, taken supplementally for the identical samples, the
above features are well understood that phonons are strongly scattered by spin
solitons and that \kappa in the I phase is governed by their spatial
distribution. In particular, the plateau feature in the doped samples suggests
"freezing" of the solitons, in which antiferromagnetism must be playing an
essential role because this feature is absent at temperatures above T_N.
