We discuss some new features of the model of two two-level atoms interacting with two single-mode thermal cavity field via multi-photon transitions under intensity-dependent coupling. We examine the dynamics of quantum and classical correlations of the system initially exists in Werner states. The results show that the sudden death and sudden birth of quantum entanglement occur but the geometric measure of quantum discord remains non-zero. It is observed that, by increasing the number of photons, the periods become shorter and the quantum discord and entanglement become irregular.