  We have measured the thermal conductivity parallel to the a-axis of the
Zn-free and 1% Zn-substituted SrCu$_{2-x}$Zn$_x$(BO$_3$)$_2$ in magnetic fields
up to 14 T, in order to examine the thermal conductivity due to the
multi-triplet magnons. It has been found that the thermal conductivity peak
observed in the spin gap state is suppressed by the substitution of Zn for Cu
in high magnetic fields above 6 T, while it is not changed in low magnetic
fields below 6 T. The results suggest that the thermal conductivity peak in the
spin-gap state of SrCu$_2$(BO$_3$)$_2$ is composed of not only thermal
conductivity due to phonons but also that due to the multi-triplet magnons in
high fields above 6 T.
