Cells maintain homeostasis via dynamic regulation of stress response pathways. Stress pathways transiently induce response regulons via negative feedback loops, but the extent to which individual genes provide feedback has not been comprehensively measured for any pathway. Here, we disrupted the induction of each gene in the Saccharomyces cerevisiae heat shock response (HSR) and quantified cell growth and HSR dynamics following heat shock. The screen revealed a core feedback loop governing the expression of the chaperone Hsp70 reinforced by an auxiliary feedback loop controlling Hsp70 subcellular localization. Mathematical modeling and live imaging demonstrated that multiple HSR targets converge to promote Hsp70 nuclear localization via its release from cytosolic condensates. Following ethanol stress, a distinct set of factors similarly converged on Hsp70, suggesting that nonredundant subsets of the HSR regulon confer feedback under different conditions. Flexible spatiotemporal feedback loops may broadly organize stress response regulons and expand their adaptive capacity.