  We develop the thermodynamics of black holes in AdS$_4$ and AdS$_7$ near
their BPS limit. In each setting we study the two distinct deformations
orthogonal to the BPS surface as well as their nontrivial interplay with each
other and with BPS properties. Our results illuminate recent microscopic
calculations of the BPS entropy. We show that these microscopic computations
can be leveraged to also describe the near BPS regime, by generalizing the
boundary conditions imposed on states.
