Lattice stability in a model of an antiferromagnetic ring coupled to adiabatic phonons is investigated for different values of the spin and numbers of magnetic sites. The magnetoelastic transition is shown to be heavily affected by the spin value, displaying a qualitative difference in the nature of the instability for spin one-half. Among the different synthesized materials, Cu8 seems to be the best candidate to observe lattice dimerization in these systems. Our analysis excludes stable lattice distortions in higher spin rings. The effects of thermal fluctuations are studied in the Cu8 model, where a characteristic crossover temperature is estimated.