I consider quantum quenches in the spin-1/2 Heisenberg XXZ chain, starting from initial thermal density matrices. The spreading of correlations is investigated by computing connected spin correlations using matrix product methods. The spreading velocities are observed to vary substantially with the initial density matrix, but a striking data collapse when the spreading velocity is plotted against the final state energy density. These findings are explained by constructing ``particle'' and ``hole'' excitations in an appropriately defined generalised micro-canonical ensemble using the integrability of the XXZ chain.