 Kerr-Newman horizon temperature

The outer-horizon surface gravity is $(r_{+}-r_{-})/(2(r_{+}^2+a^2))$. Hawking radiation or nondegenerate Euclidean black-hole regularity condition gives $T_H=\kappa /(2\pi )$ in units $G=\hslash =c=k_B=1$. The zero-temperature extremal value is the nonextremal limit; conical regularity alone does not fix a Euclidean period at a degenerate horizon.