  We study thermal states of strongly interacting quantum spin chains and prove
that those can be represented in terms of convex combinations of matrix product
states. Apart from revealing new features of the entanglement structure of
Gibbs states our results provide a theoretical justification for the use of
White's algorithm of minimally entangled typical thermal states. Furthermore,
we shed new light on time dependent matrix product state algorithms which yield
hydrodynamical descriptions of the underlying dynamics.
