In this article, we present a continuum mechanics based approach for modeling thermally induced single-nanoparticle phase transitions studied in ultrafast electron microscopy. By using coupled differential equations describing heat transfer and the kinetics of the phase transition, we determine the major factors governing the time scales and efficiencies of thermal switching in individual spin-crossover nanoparticles, such as the thermal properties of the (graphite) substrate, the particle thickness, and the interfacial thermal contact conductance between the substrate and the nanoparticle. By comparing the simulated dynamics with the experimental single-particle diffraction time profiles, we demonstrate that the proposed non-equilibrium phase transition model can fully account for the observed switching dynamics.