  We study of the effect of turbulence on diffusion processes within magnetized
medium. While we exemplify our treatment with heat transfer processes, our
results are quite general and are applicable to different processes, e.g.
diffusion of heavy elements. Our treatment is also applicable to describing the
diffusion of cosmic rays arising from magnetic field wandering. In particular,
we find that when the energy injection velocity is smaller than the Alfven
speed the heat transfer is partially suppressed, while in the opposite regime
the effects of turbulence depend on the intensity of driving. In fact, the
scale $l_A$ at which the turbulent velocity is equal the Alfven velocity is a
new important parameter. When the electron mean free path $\lambda$ is larger
than $l_A$, the stronger the the turbulence, the lower thermal conductivity by
electrons is. The turbulent motions, however, induces their own advective
transport, that can provide effective diffusivity. For clusters of galaxies, we
find that the turbulence is the most important agent for heat transfer. We also
show that the domain of applicability of the subdiffusion concept is rather
limited.
