  Bosonic condensation of microcavity polaritons is accompanied by their
relaxation from the ensemble of excited states into a single quantum state. The
excess of energy is transferred to the crystal lattice that eventually involves
heating of the structure. Creation of the condensate results in the local
increase of the temperature which leads to the red shift of the exciton energy
providing the mechanism for polariton self-trapping. By employing the
driven-dissipative Gross-Pitaevskii model we predict a new type of a stable
localized solution supported by the thermally-induced self-trapping in a
one-dimensional microcavity structure. The predicted solution is of a sink-type
i.e. it is characterized by the presence of converging density currents. We
examine the spontaneous formation of these states from the white noise under
spatially localized pumping and analyze the criteria for their stability. The
collective bosonic polaron state described here may be considered as a toy
model for studies of bosonic stars formed due to the self-gravity effect.
