<p>We study a model consisting of an isolated two-level atom and two two-level atoms (qubits) trapped in a lossless cavity and resonantly interacting with a single-mode thermal electromagnetic field through many-photon transitions. This system is of significant interest in the field of cavity quantum electrodynamics and quantum information processing and can be realized in superconducting Josephson circuits in coplanar cavities, Rydberg atoms in cavities, etc. We obtained an exact analytical solution for the evolution operator of the considered model. On its basis, we derived the time-dependent density matrixes for initial W- or GHZ-type atomic states and thermal cavity state. With the help of pairwise concurrence and fidelity, we investigated the dynamics of entanglement in the considered model. We showed that in the nonlinear many-photon processes starting from W-type states, the atomic entanglement is stronger than that in the linear one-photon processes. We also obtained for considered initial states that the phenomenon of sudden death of entanglement (ESD) can be eliminated for large photon multiples. We also showed that for the initial GHZ-state the long-lived entangled states for large values of photon multiples can be generated.</p>