Thermal conductivity \kappa is measured at very low temperatures down to 0.28 K for pure and Mg-doped CuGeO_3 single crystals. The doped samples carry larger amount of heat than the pure sample at the lowest temperature. This is because antiferromagnetic magnons appear in the doped samples and are responsible for the additional heat conductivity, while \kappa of the pure sample represents phonon conductivity at such low temperatures. The maximum energy of the magnon is estimated to be much

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... than the spin-Peierls-gap energy. The result presents the first example that \kappa at very low temperatures probes the magnon transport in disorder-induced antiferromagnetic phase of spin-gap systems.