  We show that the critical temperature of a ferromagnetic phase transition in
a quasi-two-dimensional hole gas confined in a diluted magnetic semiconductor
quantum well strongly depends on the hole chemical potential and hole density.
The significant variations of the the Curie temperature occur close to the
Lifshitz topological transition points where the hole Fermi surface acquires
additional components of topological connectivity due to the filling of excited
size-quantization subbands. The model calculations demonstrate that the Curie
temperature can be doubled by a small variation of the gate voltage for the
CdMnTe/CdMgTe quantum well based device.
