  GeSe and SnSe monochalcogenide monolayers and bilayers undergo a
two-dimensional phase transition from a rectangular unit cell to a square unit
cell at a temperature $T_c$ well below the melting point. Its consequences on
material properties are studied within the framework of Car-Parrinello
molecular dynamics and density-functional theory. No in-gap states develop as
the structural transition takes place, so that these phase-change materials
remain semiconducting below and above $T_c$. As the in-plane lattice transforms
from a rectangle onto a square at $T_c$, the electronic, spin, optical, and
piezo-electric properties dramatically depart from earlier predictions. Indeed,
the $Y-$ and $X-$points in the Brillouin zone become effectively equivalent at
$T_c$, leading to a symmetric electronic structure. The spin polarization at
the conduction valley edge vanishes, and the hole conductivity must display an
anomalous thermal increase at $T_c$. The linear optical absorption band edge
must change its polarization as well, making this structural and electronic
evolution verifiable by optical means. Much excitement has been drawn by
theoretical predictions of giant piezo-electricity and ferroelectricity in
these materials, and we estimate a pyroelectric response of about $3\times
10^{-12}$ $C/K m$ here. These results uncover the fundamental role of
temperature as a control knob for the physical properties of few-layer group-IV
monochalcogenides
