Extrinsic spinon scattering by defects and phonons instead of intrinsic spinon-spinon coupling is responsible for resistive magnetic heat transport in one-dimensional (1D) quantum magnets. Here we report an investigation of the elusive extrinsic effect in the 1D Heisenberg S=1/2 spin chain compound Ca_{2}CuO_{3}, where the defect concentration is determined from the measured specific heat and first-principles calculations are used to separate the lattice component of the measured thermal conductivity to isolate a large magnetic contribution (κ_{m}). The obtained temperature-dependent spinon-defect and spinon-phonon mean free paths can enable a quantitative understanding of both κ_{m} and the spinon-induced spin Seebeck effect.