It was recently proposed that there exist stable supersymmetric phases for
finite temperature superstings. This issue was investigated using an effective
supergravity which takes into account massive winding modes. Such a theory
admits BPS solutions that do not suffer from Hagedorn-type instabilities. We
extend several aspects of this work. First we restrict to the real-field sector
of the theory and allow, in general, for unequal right and left winding fields.
Then, by further specializing to type-II theories (IIA, IIB and a self-dual
hybrid) we construct the most general 1/2-BPS solution and reveal several new
features arising in various consistent truncations. In the heterotic case we
investigate the general properties of the solution which is presented in a
closed form in the limit of infinitely large left-winding field.Comment: 19 pages, latex. v2: clarifying remarks are added and a few typos are
corrected, version to appear in JHE