  Recent work has shown that loop corrections from massless particles generate
$\frac{3}{2}\log T_{\text{Hawking}}$ corrections to black hole entropy which
dominate the thermodynamics of cold near-extreme charged black holes. Here we
adapt this analysis to near-extreme Kerr black holes. Like AdS$_2\times S^2$,
the Near-Horizon Extreme Kerr (NHEK) metric has a family of normalizable zero
modes corresponding to reparametrizations of boundary time. The path integral
over these zero modes leads to an infrared divergence in the one-loop
approximation to the Euclidean NHEK partition function. We regulate this
divergence by retaining the leading finite temperature correction in the NHEK
scaling limit. This "not-NHEK" geometry lifts the eigenvalues of the zero
modes, rendering the path integral infrared finite. The quantum-corrected
near-extremal entropy exhibits $\frac{3}{2}\log T_{\text{Hawking}}$ behavior
characteristic of the Schwarzian model and predicts a lifting of the ground
state degeneracy for the extremal Kerr black hole.
