There is no string thermal path-integral, gravity is incompatible with a uniform constant energy density. Constant energy density, constant temperature, leads to gravitational collapse when the volume is too big. This is why you can't have a consistent string thermal equilibrium state.

One consequence of this is that it is not possible to speak about thermal analogs of T-duality clearly in flat space-time, as people sometimes try to do, using imaginary time periodic path integrals. The presence of a thermal energy density curves space, and constant energy density is inconsistent.

The closest analog of a pure thermal state in a gravitational theory is a deSitter space, because semiclassically this space has a constant temperature, and a uniform cosmological constant. This type of state is not easy to incorporate into string theory, there is no consensus on how to do it.