  We find new black 3-brane solutions describing the "conifold gauge theory" at
nonzero temperature and baryonic chemical potential. Of particular interest is
the low-temperature limit where we find a new kind of weakly curved
near-horizon geometry; it is a warped product AdS_2 x R^3 x T^{1,1} with warp
factors that are powers of the logarithm of the AdS radius. Thus, our solution
encodes a new type of emergent quantum near-criticality. We carry out some
stability checks for our solutions. We also set up a consistent ansatz for
baryonic black 2-branes of M-theory that are asymptotic to AdS_4 x Q^{1,1,1}.
