  In this paper, we discuss the important question of how to extrapolate a
given zero-temperature string model to finite temperature. It turns out that
this issue is surprisingly subtle, and we show that many of the standard
results require modification. For concreteness, we focus on the case of the
ten-dimensional SO(32) heterotic string, and show that the usual
finite-temperature extrapolation for this string is inconsistent at the level
of a proper worldsheet theory. We then derive the proper extrapolation, and in
the process uncover a universal Hagedorn temperature for all tachyon-free
closed string theories in ten dimensions --- both Type II and heterotic. As we
discuss, these results are not in conflict with the well-known exponential
growth in the degeneracies of string states in such models. This writeup is a
concise summary of our recent paper hep-th/0505233, here presented using a
``bottom-up'' approach based on determining self-consistent finite-temperature
extrapolations of zero-temperature string models. Some new results and
observations are also added.
