  Based on the path integral representation of the partition function of a many
body system with separable two body interaction we propose a systematic
extension of the perturbed static path approximation (PSPA) to lower
temperatures. Thereby, special attention must be paid to instabilities of the
classical mean field solution in functional space that cause divergencies
within the conventional PSPA. As a result we develop an approximation
applicable from high to very low temperatures. These findings are tested
against exact results for the archetypical cases of a particle moving in a one
dimensional double well and the exactly solvable Lipkin model. In particular,
we obtain a very good approximation to the level density of the Lipkin model
even at low thermal excitations. Our results may have potential applications in
low temperature nuclear physics and mesoscopic systems, e.g. for gap
fluctuations in nanoscale superconducting devices previously studied within a
PSPA type of approximation.
  PACS: 5.30.-d, 24.60.-k, 21.10.Ma, 74.25.Bt
