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.