The polypeptide-coding mRNAs are coated by specialized proteins at any stage of their lifecycle. One of few circumstances when free mRNA appears in the cytosol is the disassembly of polysomes during stress-induced shutdown of protein synthesis. Using quantitative mass spectrometry, we identified free RNA interactors in the heat-shocked mammalian cells and reconstituted the protein-RNA association in vitro. RNA-associated proteins displayed higher disorder and larger size, which supports the role of multivalent interactions during the initial phase of the RNA granule formation. Structural features of the free RNA interactors defined them as a subset of RNA-binding proteins. Our results reveal how free RNA can participate in reorganization of cellular functions during proteostasis stress.