  Quantum stochastic methods based on effective wave functions form a framework
for investigating the generally non-Markovian dynamics of a quantum-mechanical
system coupled to a bath. They promise to be computationally superior to the
master-equation approach, which is numerically expensive for large dimensions
of the Hilbert space. Here, we numerically investigate the suitability of a
known stochastic Schr\"odinger equation that is local in time to give a
description of thermal relaxation and energy transport. This stochastic
Schr\"odinger equation can be solved with a moderate numerical cost, indeed
comparable to that of a Markovian system, and reproduces the dynamics of a
system evolving according to a general non-Markovian master equation. After
verifying that it describes thermal relaxation correctly, we apply it for the
first time to the energy transport in a spin chain. We also discuss a portable
algorithm for the generation of the coloured noise associated with the
numerical solution of the non-Markovian dynamics.
