  We derive a closed form expression for the sum of all the infrared divergent
contributions to the free-energy of a gas of gravitons. An important ingredient
of our calculation is the use of a gauge fixing procedure such that the
graviton propagator becomes both traceless and transverse. This has been shown
to be possible, in a previous work, using a general gauge fixing procedure, in
the context of the lowest order expansion of the Einstein-Hilbert action,
describing non-interacting spin two fields. In order to encompass the problems
involving thermal loops, such as the resummation of the free-energy, in the
present work, we have extended this procedure to the situations when the
interactions are taken into account.
