  In hep-th/0508024, noncritical M-theory for two-dimensional Type 0A and 0B
strings was defined in terms of a double-scaled theory of nonrelativistic
fermions in 2+1 dimensions. Here we study this noncritical M-theory at finite
temperature. We derive the exact expression for the free energy of its vacuum
solution, as a function of a coupling constant $g_M$ and the radius $R$ of the
thermal circle. We show that at high temperature, the theory is effectively
described by another M-theory solution, whose effective loop-counting coupling
scales in a novel way characteristic of M-theory, as $T^3$. Our calculations
further suggest that noncritical M-theory is dual to the closed string theory
of the topological A-model on a Calabi-Yau, with the radius $R$ of the
Euclidean time circle in M-theory playing the role of the string coupling
constant of the A-model. In this correspondence, T-duality on the Euclidean
time circle of noncritical M-theory implies an S-duality for the topological
A-model.
