This paper focuses on the utilization of local radial basis functions (LRBFs) based level set method (LSM) for topology optimization of two-dimensional thermal problems using both concentrated as well as uniformly distributed heat generation. The design domain is embedded implicitly into a higher-dimensional function, which is parametrized with the LRBFs through an explicit scheme. This novel combination of LRBFs and LSM has the capability of controlling the topological variations automatically, i.e., hole insertion, merging with each other and with the boundary. The governing equations of heat conduction system are solved with the finite element method to obtain the sensitivities at level set grid points as a velocity field for evolution of the structural geometry. The objective function is set to the heat transfer potential with the maximum material volume as the design constraint. Several experiments are conducted on benchmark test problems and the resulting optimal solutions reveals efficiency, convergence and good agreement with those reported in the literature.