We investigate the quantum sensing performance of a dephasing qubit as a probe in Ohmic-family environments, characterized by the coupling strength $\eta$, the Ohmicity parameter $s$, and the cutoff frequency ${\omega }_c$ to be estimated. The performance is quantified by the dimensionless quantum signal-to-noise ratio $\mathcal{Q}$. We show that the evolution of $\mathcal{Q}$ with the scaled time ${\omega }_{c}t$ is independent of ${\omega }_c$, and peaks at an optimal time $t_{\text{opt}}$, yielding optimal sensitivity ${\mathcal{Q}}_{\text{opt}}$. We analyze how ${\mathcal{Q}}_{\text{opt}}$ depends on $\eta , s$, and the temperature $T$. Our results demonstrate that, for any Ohmic-family environment, provided that ${\omega }_c{t}_{\text{opt}}\ll 1, {\mathcal{Q}}_{\text{opt}}$ always reaches the upper bound, ${\mathcal{Q}}_{\text{max}}=0.648$ at zero temperature, and consistently attains ${\mathcal{Q}}_{\text{max}}/4$ at high temperatures. Remarkably, we find that increasing the scaled temperature $T/{\omega }_c$ can enhance ${\mathcal{Q}}_{\text{opt}}$ by nearly two orders of magnitude compared to its zero-temperature counterpart for certain Ohmic-family environments. Our work reveals that temperature can serve as a resource to enhance sensing precision, as it accelerates the encoding of the cutoff frequency information into the probe state, thereby enabling optimal measurement within a short time window.

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• Quantum parameter estimation
• Quantum sensing