  Equilibrium states of infinite extended lattice systems at high temperature
are studied with respect to their entanglement. Two notions of separability are
offered. They coincide for finite systems but differ for infinitely extended
ones. It is shown that for lattice systems with localized interaction for high
enough temperature there exists no local entanglement. Even more quasifree
states at high temperature are also not distillably entangled for all local
regions of arbitrary size. For continuous systems entanglement survives for all
temperatures. In mean field theories it is possible, that local regions are not
entangled but the entanglement is hidden in the fluctuation algebra.
