Subnanometric cobalt metallic particles, with an average size of 0.8 nm and an estimated number of 50 atoms, have been stabilized in the confined spaces within the nanopores of crystalline molecular sieves. Remarkably, these clusters show a rapid vanishing of the magnetization as the temperature is increased from 10 to 20 K because of the ferromagnetic-paramagnetic transition together with thermal fluctuations of the remaining moment. This dramatic reduction of the transition temperature is due to strong finite size effects. Such behavior, predicted for very small metallic particles, was never observed before due to the inherent difficulty in achieving subnanometric stable metallic particles.