Abstract <p>We study neutrino clusters formed owing to the interaction of neutrinos with a light scalar boson. This interaction is attractive. We consider one of the model of the cluster cooling, which must provide the energy losses by the neutrino gas during its compression while a cluster is formed. Assuming that a cluster appears in the early Universe after the electroweak phase transition, we suggest that the neutrino gas is cooled owing to the emission of Cherenkov plasmons. We establish the temperature interval where the cluster cooling rate is greater than that of the Universe expansion. Thus, the temperature of the neutrino gas inside the cluster drops to the temperature of relic neutrinos. Moreover, we find that the neutrino decoupling temperature is within this interval. Thus, thermal fluctuations of the electroweak plasma do not affect the cluster formation.</p>