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We investigate the cooling–heating phase transition of the Euler–Heisenberg-AdS black hole. First, the black hole thermodynamic quantities and the state equation are reviewed. Then, we research cooling–heating phase transition and further plot the inversion and isenthalpic curves in the T–P plane. Meanwhile, we find that the inversion temperature gradually decreases with the increase of Euler–Heisenberg parameter a for the inversion curves, while this parameter has no effect in the cooling region, and the isenthalpic curves gradually move to the positive direction of X-axis with the increase of Euler–Heisenberg parameter a in the heating region. In particular, the inversion temperature and pressure of this black hole are negative, we deem that this case is caused by the vacuum polarization and the quantum electrodynamics corrections, which makes the electromagnetic energy (repulsion force) produced by the black hole shield the gravity produced by the black hole mass. In addition, this explanation has been mentioned in previous studies [M. Daniela and B. Nora, Phys. Rev. D 102, 084011 (2020); R. Ruffini, Y. B. Wu and S. S. Xue, Phys. Rev. D 88, 085004 (2013)]. [ABSTRACT FROM AUTHOR]