  It has been argued by Iliesiu, Kologlu and Turiaci in arXiv:2107.09062 that
one can compute the supersymmetric index of black holes using black hole
geometry carrying finite temperature but a specific complex angular velocity.
We follow their prescription to compute the logarithmic correction to the
entropy of BPS states in four dimensions, defined as the log of the index of
supersymmetric black holes, and find perfect agreement with the previous
results for the same quantity computed using the near horizon $AdS_2 \times
S^2$ geometry of zero temperature black holes. Besides giving an independent
computation of supersymmetric black hole entropy, this analysis also provides a
test of the procedure used previously for computing logarithmic corrections to
Schwarzschild and other non-extremal black hole entropy.
