The heat shock response (HSR) is a fundamental cellular mechanism that ensures protein homeostasis under thermal stress. This study presents a dynamical systems model to investigate how cells regulate HSR under gradual and acute temperature changes. Using an ordinary differential equation (ODE)-based framework, we integrate key molecular components, including heat shock proteins (HSPs), transcriptional regulators, and misfolded proteins, to simulate stress adaptation dynamics. Our analysis reveals distinct regulatory strategies: While gradual temperature increases lead to a preemptive adaptation, acute heat shocks induce a transient but intense stress response. The predictions of the model align with the experimental data, demonstrating its ability to simulate genetic perturbations and environmental fluctuations. These findings provide a quantitative perspective on cellular resilience mechanisms, offering new insight into the system-level regulation of stress adaptation and its broader implications in biotechnology and medicine.