  In this paper, which is a companion to ArXiv:1204.2711[hep-th], we formulate
a criterion for constructing 11D/10D maximal supergravity black-brane solutions
with the near-extremal $S\sim n^3T^5$ entropy-temperature relation. We present
explicit examples of such solutions with special attention paid to
thermodynamics of black M-waves (KK-waves), intersecting/interpolating black
branes with KK-waves, M2/M5 branes and their descents. We find the conditions
on charges and numbers of branes in intersections, under which the dielectric
effect of brane polarization becomes manifest on the supergravity side. We also
briefly discuss the shear viscosity per entropy bound of M5 and D4 black branes
within the AdS/CFT hydrodynamical limit.
