  We recast the study of a closed string gas in a toroidal container in the
physical situation in which the single string density of states is independent
of the volume because energy density is very high. This includes the gas for
the well known Brandenberger-Vafa cosmological scenario. We describe the gas in
the grandcanonical and microcanonical ensembles. In the microcanonical
description, we find a result that clearly confronts the Brandenberger-Vafa
calculation to get the specific heat of the system. The important point is that
we use the same approach to the problem but a different regularization. By the
way, we show that, in the complex temperature formalism, at the Hagedorn
singularity, the analytic structure obtained from the so-called
F-representation of the free energy coincides with the one computed using the
S-representation.
