Differences in the physical interactions between proteins, such as binding equilibria, can provide clues about the differences in their function. The binding of heat shock proteins to substrate proteins in living cells is one such example. Eukaryotic cells have evolved many homologues in the Hsp70 family of heat shock proteins, each of which is specialized for a specific function. We previously showed that Hsp70, which is upregulated during heat shock, binds to the model substrate phosphoglycerate kinase (PGK) in human cells before PGK completely unfolds. We dubbed this the "preemptive holding" mechanism. Here, we studied the homologue Hsc70 (heat shock cognate protein), which is constitutively expressed in human cells even in the absence of heat shock. Recent literature has demonstrated the multiple functions performed by Hsc70 in cells under normal conditions. Despite the name "heat shock cognate", very few studies have shown whether Hsc70 is actually involved in the heat shock response. Here we corroborate the existence of the in-cell heat shock response of Hsc70. We show that Hsc70 binds to PGK in human cells in a cooperative manner that directly correlates with protein thermal unfolding. This "unfolded state holding" mechanism differs from the Hsp70 "preemptive holding" mechanism. We rationalize this difference by protein evolution; unlike Hsp70, which is upregulated in order to bind proteins specifically during heat shock, the finite amount of Hsc70 in cells cannot afford to bind to still-folded proteins without compromising its multiple other functions.