  We study the microcanonical density of states and the thermal properties of a
bosonic string gas starting from a calculation of the Helmholtz free energy in
the S-representation. By adding more and more strings to the single string
system, we induce that, for infinite volume, there is no negative specific heat
region but a transition at a finite value of the energy per string from the low
energy regime to a region of infinite specific heat at the Hagedorn
temperature. Forcing the description of this phase in terms of strings gives a
picture in which there is a very fat string in a sea of low energetic ones. We
argue that the necessary changing of this description should not change the
fact that perturbatively $T_H$ is a maximum temperature of the system.
