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A boundary dispatch Monte Carlo method, in which the particle are dispatched from the boundaries of conductive media or sources of heat, is developed. A fixed number of particles are dispatched from a boundary node to he nearest internal node. These particles make random walk within the medium similar to that of the conventional Monte Carlo method. Once a particle visits an internal node, a number equal to the temperature of the boundary node from which particles are dipatched is added to a flag. Performing this procedure for all boundary nodes, the temperature of a node can be determined by dividing the flag of this node by the total number of particle visits to this node. The results of this approach based on the Exodus dispatching method compare well with the Gauss-Seidel method. Its computational time is less than the shrinking boundary Exodus method. The results of this approach are presented for a number of conduction problems. Procedures for treating different boundary conditions and internal heat generation are also presented in the manuscript.