  We present initial results from ongoing lattice investigations into the
thermal phase structure of the Berenstein--Maldacena--Nastase deformation of
maximally supersymmetric Yang--Mills quantum mechanics. The phase diagram of
the theory depends on both the temperature $T$ and the deformation parameter
$\mu$, through the dimensionless ratios $T / \mu$ and $g \equiv \lambda /
\mu^3$ with $\lambda$ the 't Hooft coupling. Considering couplings $g$ that
span three orders of magnitude, we reproduce the weak-coupling perturbative
prediction for the deconfinement $T / \mu$ and approach recent large-$N$ dual
supergravity analyses in the strong-coupling limit. We are carrying out
calculations with lattice sizes up to $N_{\tau} = 24$ and numbers of colors up
to $N = 16$, to allow initial checks of the large-$N$ continuum limit.
