The cosmic reheating is an important epoch in the very early Universe and has significant impacts on the primordial black hole (PBH) abundance and the scalar-induced gravitational wave (SIGW) spectrum. The relevant energy scale and the constituents of cosmic medium are encoded in the reheating frequency $f_{\mathrm{reh}}$ and the equation of state parameter $w$. In this work, we perform a full parameter space Bayesian inference, using the NANOGrav 15-yr dataset to constrain the thermal history of reheating. Treating $f_{\mathrm{reh}}$ and $w$ as free parameters, we systematically investigate the Dirac $\delta$, narrow, and broad log-normal primordial power spectra. Current pulsar timing array data can effectively constrain the peak frequency of the SIGW spectrum as $f_{\mathrm{p}}\sim {10}^{-7.6}-{10}^{-7.0}\mathrm{Hz}$, along with $f_{\mathrm{reh}}\sim {10}^{-9.0}-{10}^{-8.3}\mathrm{Hz}$ and $w\sim 0.19–0.79$ (the 68% confidence level), when the power spectrum has a relatively narrow width $\mathrm{\Delta }\lesssim 1$. A broader power spectrum introduces a smoothing effect that obscures the characteristic frequency knee in the SIGW spectrum, leading to the loss of information about cosmic reheating. Furthermore, for the Dirac $\delta$ and narrow spectra, the PBH masses associated with the SIGWs are anchored at the planetary mass scale around ${10}^{-6}-{10}^{-4}{M}_{\odot }$. This establishes a consistent physical framework that naturally bridges the nanohertz gravitational wave background with the dark matter candidates implied by the Optical Gravitational Lensing Experiment microlensing events.

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• Gravitational waves
• Inflation