The network of potential minima and transition states for the Lennard-Jones-38 (LJ38) cluster created by Wales’s group exemplifies a large stochastic network with detailed balance and temperature-dependent pairwise transition rates. I will discuss some computational tools for the zero- and the finite-temperature analysis of the transition process between two given states of such a network. The asymptotic zero-temperature pathway and its range of validity, as well as an effective description of the transition process beyond this range, and an explanation for the temperature-dependence of the transition rate for the LJ38 will be presented.