  Well known results in string thermodynamics show that there is always a
negative specific heat phase in the microcanonical description of a gas of
closed free strings whenever there are no winding modes present. We will
carefully compute the number of strings in the gas to show how this negative
specific heat is related to the fact that the system does not have
thermodynamic extensivity. We will also discuss the consequences for a system
of having a microcanonical negative specific heat versus the exact result that
such a thing cannot happen in any canonical (fixed temperature) description.
