An ensemble of N noninteracting spins being in thermal equilibrium and coupled to the resonant mode of a lossless microwave cavity is studied as the function of the spin temperature τ. Near τ = 0 the system is known to be in a coupled spin-photon state that manifests itself by the splitting of the cavity mode (vacuum Rabi splitting). The cavity emission spectrum is simulated for arbitrary τ. A critical temperature τ_C = ω_S N~(1/2)/2, where ω_S is the spin excitation energy, is related to the destruction of the strong coupling regime as a consequence of thermal excitations arising within the spin ensemble.
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