  We propose a model, which naturally explains an unusual thermal X-ray
emission, observed from PSR J1119-6127. The model is based on the assumption
that the pulsar magnetic field near the stellar surface differs significantly
from the pure dipole field. We show that the structure and curvature of the
field lines can be of the kind that allows the pair creation in the closed
field line region. The created pairs propagate along the closed field lines and
heat the stellar surface beyond the local poles. It is demonstrated that such a
configuration can be easily realized.
