Global warming exposes plants to severe heat stress, with consequent crop yield reduction. Organisms exposed to high temperature stresses typically protect themselves with a heat shock response (HSR), where accumulation of unfolded proteins initiates the synthesis of heat shock proteins through the heat shock transcription factor HSF1. While the molecular mechanisms are qualitatively well characterized, our quantitative understanding of the underlying dynamics is still very limited. Here, we study the dynamics of HSR in the photosynthetic model organism Chlamydomonas reinhardtii with a data-driven mathematical model of HSR. We based our dynamical model mostly on mass action kinetics, with a few nonlinear terms. The model was parametrized and validated by several independent datasets obtained from the literature. We demonstrate that HSR quantitatively and significantly differs if an increase in temperature of the same magnitude occurs abruptly, as often applied under laboratory conditions, or gradually, which would rather be expected under natural conditions. In contrast to rapid temperature increases, under gradual changes only negligible amounts of misfolded proteins accumulate, indicating that the HSR of C. reinhardtii efficiently avoids the accumulation of misfolded proteins under conditions most likely to prevail in nature. The mathematical model we developed is a flexible tool to simulate the HSR to different conditions and complements the current experimental approaches.