  The low-temperature thermal conductivity (\kappa) of GdFeO_3 single crystals
is found to be strongly dependent on magnetic field. The low-field \kappa (H)
curves show two "dips" for H \parallel a and only one "dip" for H \parallel c,
with the characteristic fields having good correspondence with the spin-flop
and the spin-polarization transitions. A remarkable phenomenon is that the
subKelvin thermal conductivity shows hysteretic behaviors on the history of
applying magnetic field, that is, the \kappa(H) isotherms measured with field
increasing are larger than those with field decreasing. Intriguingly, the broad
region of magnetic field (\sim 0--3 T) showing the irreversibility of heat
transport coincides with that presenting the ferroelectricity. It is discussed
that the irreversible \kappa(H) behaviors are due to the phonon scattering by
ferroelectric domain walls. This result shows an experimental feature that
points to the capability of controlling the ferroelectric domain structures by
magnetic field in multiferroic materials.
