  Quasi-two dimensional electron systems exhibit peculiar transport effects
depending on their density profiles and temperature. A usual two dimensional
electron system is assumed to have a $\delta$ like density distribution along
the crystal growth direction. However, once the confining quantum well is
sufficiently large, this situation is changed and the density can no longer be
assumed as a $\delta$ function. In addition, it is known that the density
profile is not a single peaked function, instead can present more than one
maxima, depending on the well width. In this work, the electron density
distributions in the growth direction considering a variety of wide quantum
wells are investigated as function of temperature. We show that, the double
peak in the density profile varies from symmetric (similar peak height) to
asymmetric while changing the temperature for particular growth parameters. The
alternation from symmetric to asymmetric density profiles is known to exhibit
intriguing phase transitions and is decisive in defining the properties of the
ground state wavefunction in the presence of an external magnetic field, i.e
from insulating phases to even denominator fractional quantum Hall states.
Here, by solving the temperature and material dependent Schr\"odinger and
Poisson equations self-consistently, we found that such a phase transition may
elaborated by taking into account direct Coulomb interactions together with
temperature.
