Stress granules (SGs) are among the most studied membraneless organelles that form upon heat stress (HS) to sequester unfolded, misfolded, or aggregated protein, supporting protein quality control (PQC) clearance. The folding states that are primarily associated with SGs, as well as the function of the phase separated environment in adjusting the energy landscapes, remain unknown. Here, we investigate the association of superoxide dismutase 1 (SOD1) proteins with different folding stabilities and aggregation propensities with condensates in cells, in vitro and by simulation. We find that irrespective of aggregation the folding stability determines the association of SOD1 with SGs in cells. In vitro and in silico experiments however suggest that the increased flexibility of the unfolded state constitutes only a minor driving force to associate with the dynamic biomolecular network of the condensate. Specific protein-protein interactions in the cytoplasm in comparison to SGs determine the partitioning of folding states between the respective phases during HS.