  Thermal duality, which relates the physics of closed strings at temperature T
to the physics at the inverse temperature 1/T, is one of the most intriguing
features of string thermodynamics. Unfortunately, the classical definitions of
thermodynamic quantities such as entropy and specific heat are not invariant
under the thermal duality symmetry. In this paper, we investigate whether there
might nevertheless exist special solutions for the string effective potential
such that the duality symmetry will be preserved for all thermodynamic
quantities. Imposing this as a constraint, we derive a series of unique
functional forms for the complete temperature-dependence of the required string
effective potentials. Moreover, we demonstrate that these solutions
successfully capture the leading behavior of a variety of actual one-loop
effective potentials for duality-covariant finite-temperature string ground
states. This leads us to conjecture that our solutions might actually represent
the exact effective potentials when contributions from all orders of
perturbation theory are included.
