We could use your brain :-)
I am not a thermodynamics specialist and my brain stays where it is, but is Boltzmann not applicable here ?
Heat transfer to the environment:
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html
Flow between parts:
https://www.efunda.com/formulae/heat_transfer/radiation/calc_2bodies_enclosure.cfm
Or am i thinking too simple ?
Edit: a search results in plethora of information for heat transfer by radiation or convection.
http://www.auburn.edu/academic/c