  We compute the leading logarithmic correction to black hole entropy on the
non-BPS branch of 4D ${\cal N}\geq 2$ supergravity theories. This branch
corresponds to finite temperature black holes whose extremal limit does not
preserve supersymmetry, such as the $D0-D6$ system in string theory. Starting
from a black hole in minimal Kaluza-Klein theory, we discuss in detail its
embedding into ${\cal N}=8, 6, 4, 2$ supergravity, its spectrum of quadratic
fluctuations in all these environments, and the resulting quantum corrections.
We find that the $c$-anomaly vanishes only when ${\cal N}\geq 6$, in contrast
to the BPS branch where $c$ vanishes for all ${\cal N}\geq 2$. We briefly
discuss potential repercussions this feature could have in a microscopic
description of these black holes.
