As data centers grow in scale and computing density, thermal management becomes increasingly critical. Accurate thermal modeling is essential for efficient cooling and energy optimization, yet key thermal parameters are often difficult to measure directly. This paper proposes a dynamic thermal model incorporating the central processing unit (CPU), server chassis, and air temperatures of the server room  to describe system evolution over time. Trajectory sensitivity analysis is introduced to assess the influence of each parameter and guide identifiability analysis. A nonlinear least squares problem is formulated and solved using the Levenberg-Marquardt algorithm to estimate parameters. To address limited data and structural identifiability, a subset selection method is applied to identify estimable parameters. Simulations with synthetic data validate the approach. Results show that attempting to estimate unidentifiable parameters leads to sensitivity to initial conditions and unreliable outcomes. This highlights the importance of identifiability analysis and careful parameter selection, which can be more impactful than refining estimation algorithms.

data center thermal modeling,identifiability,parameter estimation,trajectory sensitivity analysis