  We theoretically demonstrate the formation of multiple bi-stability regions
in the temperature pattern on the interface between a cuprous oxide quantum
well and DCM2:CA:PS organic compound. The Frenkel molecular exciton of the DCM2
is brought into resonance with the $1S$ quadrupole Wannier-Mott exciton in the
cuprous oxide by "solvatochromism" with CA. The resulting hybrid is thermalized
with surrounding helium bath. This leads to strongly non-linear temperature
dependence of the laser field detuning from the quadrupole exciton energy band
which is associated with the temperature induced red shift of the Wannier
exciton energy. Numerical up and down-scan for the detuning reveals
hysteresis-like temperature distribution. The obtained \emph{multiple}
bi-stability regions are at least three orders of magnitude bigger ($meV$) than
the experimentally observed bi-stability in bulk cuprous oxide ($\mu eV$). The
effective absorption curve exhibits highly asymmetrical behavior for the
Frenkel-like (above the $1S$ energy) and Wannier-like (below the $1S$ energy)
branches of the hybrid.
