  We present theoretical investigations of pressure and temperature driven
phase transitions in HgTe quantum wells grown on CdTe buffer. Using the 8-band
\textbf{k$\cdot$p} Hamiltonian we calculate evolution of energy band structure
at different quantum well width with hydrostatic pressure up to 20 kBar and
temperature ranging up 300 K. In particular, we show that in addition to
temperature, tuning of hydrostatic pressure allows to drive transitions between
semimetal, band insulator and topological insulator phases. Our realistic band
structure calculations reveal that the band inversion under hydrostatic
pressure and temperature may be accompanied by non-local overlapping between
conduction and valence bands. The pressure and temperature phase diagrams are
presented.
