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We theoretically demonstrate the formation of multiple bi-stability regionsin the temperature pattern on the interface between a cuprous oxide quantumwell and DCM2:CA:PS organic compound. The Frenkel molecular exciton of the DCM2is brought into resonance with the $1S$ quadrupole Wannier-Mott exciton in thecuprous oxide by "solvatochromism" with CA. The resulting hybrid is thermalizedwith surrounding helium bath. This leads to strongly non-linear temperaturedependence of the laser field detuning from the quadrupole exciton energy bandwhich is associated with the temperature induced red shift of the Wannierexciton energy. Numerical up and down-scan for the detuning revealshysteresis-like temperature distribution. The obtained \emph{multiple}bi-stability regions are at least three orders of magnitude bigger ($meV$) thanthe experimentally observed bi-stability in bulk cuprous oxide ($\mu eV$). Theeffective absorption curve exhibits highly asymmetrical behavior for theFrenkel-like (above the $1S$ energy) and Wannier-like (below the $1S$ energy)branches of the hybrid.

Theory of enhanced dynamical photo-thermal bi-stability effects in cuprous oxide/organic hybrid heterostructure