The discovery of Schwarz nanocrystals (SCs)—characterized by interpenetrating networks of minimal surface grain boundaries (GBs) stabilized by coherent twin boundaries (CTBs)—has pushed the boundaries of nanoscience and nanotechnology to length scales of only a few nanometers. However, the physical mechanisms governing thermal stability remain unresolved. In this talk we will introduce a free energy criterion for thermal stability of SC using large-scale thermodynamic integration, benchmarking SCs against other nanostructures like Voronoi and Kelvin nanocrystals. Surprisingly, the free energy of minimal surface GBs in SCs is higher than that of conventional GBs in Voronoi nanocrystal. Therefore, it is the significantly smaller volume fraction of GBs that reduces the overall free energy of SCs. Kinetic stabilization of SCs is accommodated by the topological interlock between CTBs and GBs. The free energy-based criterion for stability of SCs provides a rule for selecting Schwarz-like nano-structures stable at extreme conditions.