The Boltzmann Transport Equation (BTE) has been a challenging problem in many engineering fields involving particle transport for electrons, ionized molecules, phonons, etc.Phonons are quantum representations of crystal lattice vibrations excited by thermal energy. The phonon energy distribution thus represents the temperature distribution in a domain structure. A localized Kansa's method (also called localized multiquadric radial basis function collocation method) is applied to the six-dimensional BTE of phonons for thermal simulation of semiconductor nano-structures. This method is called meshless method, which is a newly developed research area in computational partial differential equations starting in the 1990’s. It has recently attracted significant attention in many fields such as fluid dynamics, solid mechanics, and computational mathematics due to its flexibility for complicated problems in high-dimensional space.  Our preliminary results show that the localized Kansa's method for the solutions of the BTE model of phonons is very effective in six-dimensional space.To the best of our knowledge, this is the first time that the BTE model of phonons is solved in six-dimensional space.