In this work we investigate the thermal entanglement between two-level atoms and photons in a NONLINEAR cavity. We consider intensity-dependent couplings and calculate the negativity, as a measure of atom-photon entanglement. The cavity is assumed to be at a temperature T, so that all number of photons, and at the same time, both atomic states, with definite probabilities, are present. We then demonstrate a condition under which the intensity-dependent coupling leads to entanglement. It is also shown that, as in the case of linear Jaynes- Cummings model, the thermal states of atoms and photons are never separable.