The heat shock response is the organized molecular response to stressors which disrupt proteostasis, potentially leading to protein misfolding and aggregation. While the regulation of the heat shock response is well-studied in single cells, its coordination at the cell, tissue, and systemic levels of a multicellular organism is poorly understood. To probe the interplay between systemic and cell-autonomous responses, we studied the upregulation of HSP-16.2, a molecular chaperone induced throughout the intestine of Caenorhabditis elegans following a heat shock, by taking longitudinal measurements in a microfluidic environment. Based on the dynamics of HSP-16.2 accumulation, we showed that a combination of heat shock temperature and duration define the intensity of stress inflicted on the worm and identified two regimes of low and high intensity stress. Modeling the underlying regulatory dynamics implicated the saturation of heat shock protein mRNA production in defining these two regimes and emphasized the importance of time separation between transcription and translation in establishing these dynamics. By applying a heat shock and measuring the response in separate parts of the animals, we implicated thermosensory neurons in accelerating the response and transducing information within the animal. We discuss possible implications of the systemic and cell level aspects and how they coordinate to facilitate the organismal response.