I don't see how stacking chips would do anything but make the heat dissipation problem much much worse. There is no magical "heat dissipating adhesive", only substances that conduct heat better or worse.
A conventional chip is a thin planar heating element attached with maximal surface area to its heat sink and we have great trouble keeping them cool now.
Heat generated internally a cubic object is more difficult to remove because the volume that is generating heat grows faster in proportion to the surface area available for removing it. I.e., the heat generation grows with the cube of the unit length and the surface only with the square).
The worst shape of all is spherical which has the highest possible ratio of volume to surface area.
Even if they managed to put heat sinks in contact with all six sides of this stack of dies, they could (at best) only remove six conventional chips' worth of heat.
Unless they have a way of circulating liquid coolant through that volume, stacking chips like that is only practical if they're almost completely off.