To 1st question:
The 1D heat flow across the layers is very similar to the Ohm's law: heat flux (W/m2) is a "currrent", temperature drop is like voltage drop, thermal resistance (thickness divided by thermal conductivity) is like electric resistance.
Transient processes inside the layer relax...
My report presented at the 15th Symposium at Boulder, CO (NIST) may be useful (unfortunately with no infrared radiation, which of course should be taken into account at such high temperatures):
http://www.lasercomp.com/List%20of%20Papers.html