Heat shock (HS) initiates rapid, extensive, and evolutionarily conserved changes in transcription that are accompanied by chromatin decondensation and nucleosome loss at HS loci. Here we have employed in situ Hi-C to determine how heat stress affects long-range chromatin conformation in human and Drosophila cells. We found that compartments and topologically associating domains (TADs) remain unchanged by an acute HS. Knockdown of Heat Shock Factor 1 (HSF1), the master transcriptional regulator of the HS response, identified HSF1-dependent genes and revealed that up-regulation is often mediated by distal HSF1 bound enhancers. HSF1-dependent genes were usually found in the same TAD as the nearest HSF1 binding site. Although most interactions between HSF1 binding sites and target promoters were established in the nonheat shock (NHS) condition, a subset increased contact frequency following HS. Integrating information about HSF1 binding strength, RNA polymerase abundance at the HSF1 bound sites (putative enhancers), and contact frequency with a target promoter accurately predicted which up-regulated genes were direct targets of HSF1 during HS. Our results suggest that the chromatin conformation necessary for a robust HS response is preestablished in NHS cells of diverse metazoan species.