  We study the violations of Bell inequality for thermal states of qubits in a
multi-qubit Heisenberg model as a function of temperature and external magnetic
fields. Unlike the behaviors of the entanglement the violation can not be
obtained by increasing the temperature or the magnetic field. The threshold
temperatures of the violation are found be less than that of the entanglement.
We also consider a realistic cavity-QED model which is a special case of the
mutli-qubit Heisenberg model.
