How is heat transferred from the core through the mantle to the crust?
It is still a little known fact that radiation play an important role in the Earth's mantle. Experiments show that mantle-material becomes transparent to infrared radiation at increasing pressures (http://www.esrf.eu/news/general-old/general-2004/earthbadro/index_html).

I would also say that the mantle is currently not understood in a way where estimates of heat-conduction-type versus depth can be accurately made. The heterogeneity of heat transfer (Cold detached subduction-slabs sinking to various depths and hot plumes quickly rising from the D''-layer) makes the question even more difficult.