Based on the earlier work for a single magnetic island and a weak stochastic magnetic field (Yu 2006 Phys. Plasmas13 062310), the heat diffusion across a local fully stochastic magnetic field is studied numerically and compared with the analytical theories. The ratio between the parallel and the perpendicular heat diffusivity, χ||/χ⊥, is found to be an important parameter in characterizing the transport. With the increase in χ||/χ⊥, the transport is dominated first by the additive effect of individual islands and then by the field ergodicity and χ||.