  We derive the free energies of both the closed heterotic, and the unoriented,
open and closed, type I string ensembles, consistent with the thermal
(Euclidean T-duality) transformations on the String/M Duality Web. A crucial
role is played by a temperature dependent Wilson line wrapping Euclidean time,
responsible for the spontaneous breaking of supersymmetry at finite temperature
while eliminating thermal tachyons, and determined uniquely by thermal duality.
Conversely, we can show that the absence of a Yang-Mills gauge sector precludes
the possibility of an equilibrium type II canonical ensemble prior to the
introduction of background Dbranes or fluxes. As a consistency check, we verify
that our results for the string free energy always reproduce the T^{10} growth
expected in the low energy field theory limits while displaying a dramatically
slower T^2 growth at temperatures above the string scale. We present both the
low and high temperature expansions for the one-loop heterotic and type I
string free energies, results which follow from an explicit term-by-term
evaluation of the modular integrals in the string mass level expansion.
