We investigate quantum parameter estimation in a two-level system interacting with a finite-temperature reservoir under measurement-based feedback control. Within the framework of a feedback-modified Markovian master equation, we derive analytical solutions for the Bloch-vector dynamics and obtain analytical expressions for the quantum Fisher information (QFI) associated with the transition frequency, the dissipation rate, and the mean thermal-occupation number. Our analysis shows that measurement-based feedback modifies the effective dissipative channels by coupling population and coherence dynamics, leading to slower coherence degradation and improved parameter sensitivity. In particular, for frequency estimation, the feedback protocol partially preserves the transverse Bloch coherence responsible for the QFI, allowing the maximum QFI to reach approximately twice that of the no-feedback case within an optimal time window, and preserving a significantly larger fraction of the ideal dissipation-free sensitivity over extended evolution times. Furthermore, the analytical results reveal a unified structure of the QFI for different estimated parameters, demonstrating that the attainable precision is governed by the combined contributions of population dynamics and quantum coherence. These results provide an analytical framework for understanding the interplay between thermal dissipation and measurement-based feedback in open-system quantum metrology and offer theoretical guidance for feedback-assisted quantum parameter estimation under realistic finite-temperature conditions.

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• Quantum feedback
• Quantum information theory