We study the second-order coherence function of a plasmonic nanoantenna fed by near-field of a single-photon source incoherently pumped in the continuous wave regime. We consider the case of a strong Purcell effect, when the single-photon source radiates almost entirely in the mode of a nanoantenna. We show that when the energy of thermal fluctuations, kT, of the nanoantenna is much smaller than the interaction energy between the electromagnetic field of the nanoantenna mode and the single-photon source, ℏΩ, the statistics of the emission is close to that of thermal radiation. In the opposite limit, ℏΩ>kT, the nanoantenna radiates single photons. In the last case, we demonstrate the possibility of overcoming the radiation intensity of an individual single-photon source. This result opens the possibility of creating a high-intensity single-photon source.