The Einstein-Euler-Heisenberg-AdS black hole has a minimum Hawking temperature; above it large black holes are stable and small ones evaporate, and the nonlinear correction leaves this phase structure intact.
Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, 1992) N
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The thermodynamic stability and phase structure of the Einstein-Euler-Heisenberg-AdS black holes
The Einstein-Euler-Heisenberg-AdS black hole has a minimum Hawking temperature; above it large black holes are stable and small ones evaporate, and the nonlinear correction leaves this phase structure intact.