  In the context of the black hole/string transition, it is useful to produce
Euclidean string backgrounds representing hot and self-gravitating strings. We
utilise analytical and numerical methods to find a smooth, stationary rotating
solution in the heterotic string theory at high temperatures. The solution
describes a spinning winding-momentum condensate living in three non-compact
dimensions, and its backreaction on the thermal cycle. At low temperatures, we
expect a transition between our solution to an analytical continuation of an
axionic Kerr black hole.
