By substituting one Cr3+(s=3/2) with Cd2+(s=0) in molecular octanuclear rings, a diluted ensemble of identical nanomagnets with a S=3/2 ground state, weakly split in zero field, is obtained. The lattice contribution and the essential parameters of the spin Hamiltonian of these uncompensated antiferromagnetic cyclic spin systems are determined by fitting specific heat data between 0.4 and 20 K in magnetic fields up to 7 T. Different entropy contributions are evaluated and results suggest a possible way of engineering molecular magnets to exploit low temperature magnetocaloric effect.