The quantum correlation (QC) of two qubits coupled to a thermal field is investigated based on measurement-induced disturbance. It is found that QC does not exist only in the entangled state. Due to the thermal parameter, QC is inhibited from vanishing and the phenomenon of the death and birth of entanglement occurs. Due to the field-mode structure, QC is equal to zero for separated qubits, whereas for a maximally entangled state, it has a periodic asymptotic behavior which does not vanish. QC and entanglement differ when the qubit state is initially in the separated or entangled state.