  One of the most intriguing features of string thermodynamics is thermal
duality, which relates the physics at temperature T to the physics at inverse
temperature 1/T. Unfortunately, the traditional definitions of thermodynamic
quantities such as entropy and specific heat are not invariant under thermal
duality transformations. In this paper, we propose several novel approaches
towards dealing with this issue. One approach yields a "bootstrap" method of
extracting possible exact, closed-form solutions for finite-temperature
effective potentials in string theory. Another approach involves extending the
usual definition of entropy by introducing additional terms which are
suppressed by powers of the string scale. At high temperatures, however, these
string corrections become significant and lead to a variety of surprising new
phenomena as the temperature is increased.
