Design of semiconducting nanomaterials with an indirect electronic bandgap is currently one of the major areas of research to obtain a high thermoelectric yield by lowering their lattice thermal conductivity. Intensive investigations on superlattices were performed to achieve this goal. However, like one-dimensional nanowires, they decrease heat transport in only one propagation direction of the phonons. Moreover, they often lead to dislocations since they are composed of layered materials with a lattice mismatch. Design of superlattices with a thermoelectric figure of merit ZT higher than unity is therefore hazardous. Self-assembly of epitaxial layers on silicon has been used for bottom-up synthesis of three-dimensional (3D) Ge quantum-dot (QD) arrays in Si for quantum-device and solar-energy applications. Using the atomic-scale 3D phononic crystal model, it is predicted that high-density 3D arrays of self-assembled Ge QDs in Si can as well show an extreme reduction of the thermal transport. 3D supercrystals of Ge QDs in Si present a thermal conductivity that can be as tiny as that of air. These extremely low values of the thermal conductivity are computed for a number of Ge filling ratios and size parameters of the 3D Si-Ge supercrystal. Owing to incoherent phonon scattering with predominant near-field effects, the same conclusion holds for supercrystals with moderate QD disordering. As a result, design of highly-efficient CMOS-compatible thermoelectric devices with ZT possibly much higher than unity might be possible. In this theoretical study, simultaneous evolution of both temperature and average distance between the Ge QDs is analyzed for a non-variable Ge filling ratio to obtain thermal-conductivity values as low as that of air (+/- 0.025 W/m/K).