  We study the confining/deconfining phase transition in the mass deformed
Yang-Mills matrix model which is obtained by the dimensional reduction of the
bosonic sector of the four-dimensional maximally supersymmetric Yang-Mills
theory compactified on the three sphere, i.e. the bosonic BMN model. The $1/D$
(with $D$ the number of matrices) expansion suggests that the model may have
two closely separated transitions. However, using a second order lattice
formulation of the model we find that for the small value of the mass
parameter, $\mu=2$, those two apparent critical temperatures merge at large
$N$, leaving only a single weakly first-order phase transition, in agreement
with recent numerical results for $\mu=0$ (the bosonic BFSS model).
