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Using the adaptive time-dependent density-matrix renormalization group method,the dynamics of entanglement and quantum discord of an one-dimensional spin-1/2 XXZ chain is studied when anisotropic interaction quenches are applied at different temperatures.The dynamics of the quantum discord and pairwise entanglement between the nearest qubits shows that the entanglement and quantum discord will first oscillate and then approach to a constant value.The quantum discord can be used to predict the quantum phase transition,while the entanglement cannot.