Theory of domain wall motion in a random medium is extended to the case whe
n the driving field is below the zero-temperature depinning threshold and t
he 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. Simila
r to the case of zero temperature, the hysteresis loop displays three dynam
ical phase transitions at increasing ac field amplitude h(0). The phase dia
gram in the 3D phase space of temperature, driving force amplitude, and fre
quency is investigated.