A Monte Carlo method is described to solve heat conduction problems with extremely heterogeneous and complicated geometry. The method is based on observation that the heat conduction equation is a special form of the neutron diffusion equation, which in turn is an approximation to the transport equation. The heat conduction equation is solved by the transport Monte Carlo method with appropriate boundary layer correction and scaling factor rendering the problem diffusive. As applications, the Monte Carlo results are obtained for randomly distributed fuel particles of a pebble, providing realistic temperature distributions (showing the kernel and graphite-matrix temperatures distinctly). The volumetric analytic solution commonly used in the literature underestimates the Monte Carlo results.