We present the first systematic study of rigidly rotating protoquark stars based on isentropic equations of state (EOS) within the density-dependent quark mass framework. Using a quasistatic equilibrium approach, we follow the Kelvin-Helmholtz evolution from hot, lepton-rich matter to a cold, catalyzed quark star (QS). Rotation substantially enhances the maximum stable mass (by up to $\sim 40\%$), equatorial radius, and key rotational observables, with the ratio of rotational kinetic to gravitational potential energy, $T_{\mathrm{kin}}/|W|$, reaching 0.18–0.19 near the Keplerian limit, indicating a heightened susceptibility to gravitational-wave–emitting instabilities. Thermal evolution introduces a clear ordering: all stellar properties peak during the lepton-rich stages and decrease monotonically as the star cools. Compared to hadronic stars, rotating proto-QSs exhibit larger radii, higher moments of inertia, and stronger quadrupolar deformation, producing a distinct signature in the mass–radius–spin plane. The EOS parameters are constrained using current astrophysical observations, including mass-radius measurements from HESS J1731–347 and PSR $\mathrm{J}0030+0451$, the high-mass constraint from PSR $\mathrm{J}0740+6620$, and mass-radius constraints inferred from GW170817. The results demonstrate that future multimessenger observations must account for both thermal history and rotation to identify quark matter in compact stars robustly.

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• General relativity
• Gravitational waves
• Neutron star cooling
• Novae & supernovae