Modeling blocking temperature in molecular magnets has been a long-standing problem in the field of molecular magnetism. We investigate this problem using a kinetic Monte Carlo (kMC) approach on an assembly of 100 000 short molecular magnetic chains (SMMCs), each of six identical spins with nearest-neighbor anisotropic ferromagnetic exchange interactions. Each spin is also anisotropic with an uniaxial anisotropy. The site spin on these SMMCs takes values 1, 3/2, or 2. Using the eigenstates of these SMMCs as the states of a Markov chain, we carry out a kMC simulation starting with an initial state in which all SMMCs are completely spin-polarized and assembled on a one-dimensional lattice so as to experience ferromagnetic spin-dipolar interaction with each other. From these simulations, we obtain the relaxation time τ r as a function of temperature and the associated blocking temperature. We study this for different exchange anisotropy, on-site anisotropy, and strength of dipolar interactions. The magnetization relaxation times show non-Arrhenius behavior for weak on-site interactions. The energy barrier to magnetization relaxation increases with an increase in on-site anisotropy, exchange anisotropy, and strength of spin dipolar interactions, more strongly on the last parameter. In all cases, the barrier saturates at large on-site anisotropy. The barrier also increases with site spin. The large barrier observed in rare-earth single ion magnets can be attributed to large dipolar interactions due to short intermolecular distances, due to their small size and large spin of the rare-earth ion in the molecule.