  We examine the conjecture that black holes violating the reverse
isoperimetric inequality have negative specific heat at constant volume $C_V$.
We test this conjecture on the family of generalized exotic Ba\~nados,
Teitelbiom and Zanelli (BTZ) black holes and find that $C_V$ can be positive
even when the reverse isoperimetric inequality is violated, providing a counter
example to the conjecture. However in all cases where $C_V$ is positive, the
specific heat at constant pressure $C_P$ is negative, indicating that
generalized exotic black holes are thermodynamically unstable, suggesting that
a broader version of the conjecture might hold.
