I think the naive expectation would be that a hot state would be highly entangled and non-separable. The non-separability is what leads to decoherence when you do a partial trace. You can arbitrarily split any multi-part Hilbert space into a "system" and an "environment" and then trace out the environment. If they are highy entangled with one another then the resulting system-without-environment will be decohered.