Using the concepts of quantum entanglement, quantum correlations and classical correlation and the method of full quantum theory, the evolution properties of quantum entanglement, quantum discord, geometrical quantum discord and classical correlation in a system of two coupled two-level atoms interacting with a single mode electromagnetic field in a thermal state are studied under the certain conditions. When the two atoms are in the separated state at the initial time, we analyze the effects of the coupling strength between the two coupled two-level atoms and a single mode radiation field in a thermal state. At the same time, we also discuss the mean photon number on the evolution properties of quantum entanglement, quantum correlations and classical correlation between the two atoms in the system. The results show that when an atom weakly coupled to thermal field, the evolution of quantum entanglement, quantum discord and geometrical quantum discord between twocoupled two-level atoms present the phenomenon of sudden death and sudden birth with the increase of the mean photon number of a single mode radiation field in a thermal state, which exhibit a collapse-revival process with gradually decreasing amplitude in the long time scale, and the evolution of classical correlation shows a stable oscillation form. When the effective coupling constant between the atom and a single mode electromagnetic field in a thermal state is stronger, the changes of quantum entanglement and quantum correlations still show the phenomenon of sudden death and sudden birth with increase of the mean photon number of a single mode radiation field in a thermal state. The four quantities are all in the form of irregular oscillation and the values of them significantly reduce in the long time scale. It is found that the other quantum corrections remain in the absence of quantum entanglement in the observed period of time.