We present results from our study of the Parallel Tempering algorithm. We e
xamine the swapping acceptance rate of a twin subensemble PT system. We use
action matching technology in an attempt to maximise the swap acceptance r
ate. We model the autocorrelation times within Parallel Tempering ensembles
in terms of autocorrelation times from Hybrid Monte Carlo. We present esti
mates for the autocorrelation times of the plaquette operator.