A special localization technique is presented for solving steady heat transfer problems, in which the thermal conductivity may depend on space variables. The original problem is split into several subproblems defined on much smaller subdomains. The subproblems are solved using the Method of Fundamental Solutions, which is a truly meshless method. This leads to a Seidel-like iterative technique, which mimics the classical Schwarz overlapping method. The problems associated with large, dense and ill-conditioned matrices are avoided. The method is embedded into a multi-level context, which significantly reduces the computational complexity.