We report low-temperature differential conductance measurements in aluminum arsenide cleaved-edge overgrown quantum wires in the pinch-off regime. At zero source-drain bias we observe Coulomb blockade conductance resonances that become vanishingly small as the temperature is lowered below $250 {\rm mK}$. We show that this behavior can be interpreted as a classical-to-stochastic Coulomb blockade cross-over in a series of asymmetric quantum dots, and offer a quantitative analysis of the temperature-dependence of the resonances lineshape. The conductance behavior at large source-drain bias is suggestive of the charge density wave conduction expected for a chain of quantum dots.