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.