Open string thermodynamics and D-branes

We study the thermodynamics of open superstrings in the presence of p-dimensional D-branes. We get some finite temperature dualities relating the one-loop canonical free energy of open strings to the self-energy of D-branes at dual temperature. For the open bosonic string the inverse dual temperature is, as expected, the dual length under T-duality, 4 pi(2) alpha'/beta. On the contrary, for the SO(N), type-I superstring the dual temperature is given by beta-duality, 2 pi(2) alpha'/beta. We also study the emergence of the Hagedorn singularity in the dual description as triggered by the coupling of the D-brane to unphysical tachyons as well as the high temperature limit.