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This paper proposes a new parameterized dynamic thermal modeling algorithm for emerging thermal-aware design and optimization for high-performance microprocessor design at architecture and package levels. Compared with existing behavioral thermal modeling algorithms, the proposed method can build the compact models from more general transient power and temperature waveforms used as training data. Such an approach can make the modeling process much easier and less restrictive than before and, thus, more amenable for practical measured data. The new method, called ParThermSID, consists of two steps. First, the response surface method based on second-order polynomials is applied to build the parameterized models at each time point for all of the given sampling nodes in the parameter space. Second, an improved subspace system identification method, called ThermSID, is employed to build the discrete state space models, by construction of the Hankel matrix and state space realization, for each time-varying coefficient of the polynomials generated in the first step. To overcome the overfitting problems of the subspace method, the new method employs an overfitting mitigation technique to improve model accuracy and predictive ability. Experimental results on a practical quad-core microprocessor show that the generated parameterized thermal model matches the given data very well. The compact models generated by ParThermSID also offer two orders of magnitude speedup over the commercial thermal analysis tool FloTHERM on the given example. The results also show that ThermSID is more accurate than the existing ThermPOF method.