The heat shock response (HSR) is a critical cellular mechanism that preserves protein homeostasis under stress. This paper presents a systems biology model that quantitatively captures the dynamic regulation of HSR under both gradual and acute thermal stress. Using an ordinary differential equation (ODE)-based framework, we integrate core molecular components—heat shock proteins (HSPs), misfolded proteins, and active transcription factors—to simulate real-time stress adaptation. Our simulations reveal that cells adopt distinct regulatory strategies depending on the thermal regime: gradual stress promotes anticipatory adaptation, while acute heat shock triggers a rapid but transient overshoot response. The model is calibrated using experimental literature and validated through sensitivity analysis, offering insights into the timing, magnitude, and feedback dynamics of proteostasis control. This work advances our understanding of thermal stress responses and provides a computational platform for hypothesis testing in cellular resilience, disease modeling, and synthetic biology applications.