  We present a model supported by simulation to explain the effect of
temperature on the conduction threshold in disordered systems. Arrays with
randomly distributed local thresholds for conduction occur in systems ranging
from superconductors to metal nanocrystal arrays. Thermal fluctuations provide
the energy to overcome some of the local thresholds, effectively erasing them
as far as the global conduction threshold for the array is concerned. We
augment this thermal energy reasoning with percolation theory to predict the
temperature at which the global threshold reaches zero. We also study the
effect of capacitive nearest-neighbor interactions on the effective charging
energy. Finally, we present results from Monte Carlo simulations that find the
lowest-cost path across an array as a function of temperature. The main result
of the paper is the linear decrease of conduction threshold with increasing
temperature: $V_t(T) = V_t(0) (1 - 4.8 k_BT P(0)/ p_c) $, where $1/P(0)$ is an
effective charging energy that depends on the particle radius and interparticle
distance, and $p_c$ is the percolation threshold of the underlying lattice. The
predictions of this theory compare well to experiments in one- and
two-dimensional systems.
