  The low-temperature thermodynamics of near-extremal rotating black holes has
recently been revisited to incorporate one-loop contributions that are dominant
in this regime. We discuss these quantum corrections to the gravitational path
integral for asymptotically Anti de-Sitter black holes in four and five
dimensions. In four dimensions we explicitly consider Kerr-AdS$_4$,
Kerr-Newman-AdS$_4$ and the rotating black hole in ${\cal N}=4$ gauged
supergravity with two scalars and two electric charges turned on. In five
dimensions we explicitly address the asymptotically flat Myers-Perry black hole
and the Kerr-AdS$_5$ black hole. In every case we find that tensor modes
contribute $\frac{3}{2} \log T_{\rm Hawking}$ to the low-temperature
thermodynamics. We identify the root cause of this universality in two facts:
(i) the universal presence of a $SL(2,\mathbb{R})$ subgroup of isometries in
the near-horizon geometry and (ii) a set of cancellations in the Lichnerowicz
operator. We show that these two conditions hold for near-extremal black holes
in asymptotically flat and asymptotically AdS spacetimes of various dimensions.
