  We have measured the thermal conductivity along the c-axis parallel to the
spin-chains, kappa_c, of the one-dimensional antiferromagnetic spin system
SrCuO_2, using as-grown and O_2-annealed single-crystals grown from raw
materials with 99.9% (3N) and 99.99% (4N) purity. The value of kappa_c around
50K, where large contribution of the thermal conductivity due to spinons,
kappa_spinon, is observed, is markedly enhanced by both the increase of the
purity of raw materials and the O_2-annealing. Therefore, the increase of
kappa_c implies that kappa_spinon is enhanced due to the decrease of spin
defects caused by impurities in raw materials and by oxygen defects. The mean
free path of spinons is as large as about 24000 angstrom at low temperatures in
the O_2-annealed single-crystal grown from raw materials with 4N purity.
