While the ground-state phase diagram of the correlated flat-band systems has been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to the experimental probes (transport, quantum capacitance, and spectroscopy) of the quantum moiré materials such as twisted bilayer graphene. Here we show, by means of momentum-space quantum Monte Carlo and exact diagonalization, in chiral limit there exists a unique thermodynamic characteristic for the correlated flat-band model with interaction-driven quantum anomalous Hall (QAH) ground state, namely, the transition from the QAH insulator to the metallic state takes place at a much lower temperature compared with the zero-temperature single-particle gap generated by the long-range Coulomb interaction. Such low transition temperature comes from the proliferation of excitonic particle-hole excitations, which transfers the electrons across the gap between different topological bands to restore the broken time-reversal symmetry and gives rise to a pronounced enhancement in the charge compressibility. Future experiments, to verify such generic thermodynamic characteristics, are proposed.