We investigate dynamics of quantum discord (QD) for two initially-correlated qubits in two independent Ohmic reservoirs at finite temperature. It is indicated that the QD changes from a constant regime to a decaying regime when the two qubits are initially prepared in X-type quantum states. In the QD constant regime, the initial QD can be preserved despite decoherence in the system. It is found that temperature difference between two reservoirs significantly affects the preservation duration (PD) of the initial QD. We show that it is possible to enhance the preservation duration by properly choosing system parameters of the two qubits and reservoir parameters. Physically, it is found that the PD of the QD can reflect the temperature inhomogeneity of the non-equilibrium system which consists of the two qubits and their reservoirs.