  We give a first principles formulation of the equilibrium statistical
mechanics of strings in the canonical ensemble, compatible with the Euclidean
timelike T-duality transformations that link the six supersymmetric string
theories in pairs. We demonstrate that each exhibits a T^2 growth in the free
energy at high temperatures far above the string scale. We verify that the low
energy field theory limit of our expression for the string free energy
reproduces the expected T^{10} growth when the contribution from massive string
modes is suppressed. In every case, heterotic, type I, and type II, we can
definitively rule out the occurrence of an exponential divergence in the
one-loop string free energy above some critical temperature. Finally, we
identify a macroscopic loop amplitude in the type I string theories which
yields the expectation value of a single Wilson-Polyakov-Susskind loop in the
low energy finite temperature supersymmetric gauge theory limit, an order
parameter for a thermal phase transition at a string scale temperature. We
point out that precise computations can nevertheless be carried out on either
side of the phase boundary by using the low energy finite temperature
supersymmetric gauge theory limits of the pair of thermal dual string theories,
type IB and type I'. Note Added (Sep 2005).
