In this paper we focus on the thermal hysteresis exhibited by spin-crossover nanocrystals with inhomogeneous interactions changing from the surface to the bulk of lattice. The model of 3D nanocrystal with ferromagnetic and antiferromagnetic coupling of the sites on the surface has been considered. The properties of size effects for ferromagnetic and antiferromagnetic surface have been analyzed in detail. Most of the features experimentally observed heretofore are reproduced by computational simulations using Monte Carlo method for Ising-like model of spin-crossover solid. The results are interpreted in terms of cooperativity.