  Theory of domain wall motion in a random medium is extended to the case when
the driving field is below the zero-temperature depinning threshold and the
creep of the domain wall is induced by thermal fluctuations. Subject to an ac
drive, the domain wall starts to move when the driving force exceeds an
effective threshold which is temperature and frequency-dependent. Similarly to
the case of zero-temperature, the hysteresis loop displays three dynamical
phase transitions at increasing ac field amplitude $h_0$. The phase diagram in
the 3-d space of temperature, driving force amplitude and frequency is
investigated.
