  Galaxy clusters exhibit regular scaling relations among their bulk
properties. These relations establish vital links between halo mass and cluster
observables. Precision cosmology studies that depend on these links benefit
from a better understanding of scatter in the mass-observable scaling
relations. Here we study the role of merger processes in introducing scatter
into the $M$-$T_{\rm X}$ relation, using a sample of 121 galaxy clusters
simulated with radiative cooling and supernova feedback, along with three
statistics previously proposed to measure X-ray surface brightness
substructure. These are the centroid variation ($w$), the axial ratio ($\eta$),
and the power ratios ($P_{20}$ and $P_{30}$). We find that in this set of
simulated clusters, each substructure measure is correlated with a cluster's
departures $\delta \ln T_{\rm X}$ and $\delta \ln M$ from the mean $M$-$T_{\rm
X}$ relation, both for emission-weighted temperatures $T_{\rm EW}$ and for
spectroscopic-like temperatures $T_{\rm SL}$, in the sense that clusters with
more substructure tend to be cooler at a given halo mass. In all cases, a
three-parameter fit to the $M$-$T_{\rm X}$ relation that includes substructure
information has less scatter than a two-parameter fit to the basic $M$-$T_{\rm
X}$ relation.
