Mesh based methods such as FEM has achieved a remarkable success in solving many engineering and science problems. However, it is widely known that the solution accuracy of these methods is largely depends on the quality of mesh generated. This becomes a serious problem when the mesh becomes distorted or changes with time. Moreover, the generation of higher order shape functions is also difficult for these methods. Due to these problems, mesh based methods are not well suited for certain types of problems such as strongly non-linear heat transfer and growth under thermo-elastic loading, etc. To overcome these problems, meshfree methods have been emerged as new computational tool. Element free Galerkin method (EFGM) is one of them. Although, a lot of literature exists on meshfree methods including few books in the area of solid mechanics, but not much literature exists in the area of heat transfer. Only few research papers are available on heat transfer using meshfree methods. Therefore, this monograph will not only provide the applications of EFGM in heat transfer but also provides the formulations along with its implementation methodology.