We investigated theoretically the thermo-induced spin transition of a nanostructure made of an active spin crossover core surrounded by an inert shell with a misfit of lattice parameters between the two constituents. We demonstrated that (i) the structural and magnetic features of the SCO core are very sensitive to the structural properties of the surrounding environment (ii) The misfit of lattice parameters influences the nature of the spin transition from gradual to abrupt one with an important shift of the transition temperature. (iii) The structural heterogeneity of the nanoparticle affects as well the spatiotemporal kinetics of the thermo-induced spin transition. The mechanical properties of the nanoparticle were as well studied and correlated with the magnetic behaviour of the nanoparticle.