Re: Physics 101
"ou may assume the 1 cc object is made from carbonized coconut, and has a surface area that is vast (Wales sized) on the microscopic scale, if you think it'll help"
I know you're trying to be helpful but the surface area matters as that is what the heat has to be conducted through. That's why a sphere is more efficient to heat than a cube, thats why people put fins on a heatsink, The conductivity matters for the same reason (copper is better than asbestos). The final heat sink and its properties matter for the same reason.
Choosing 1cc object was also fairly unhelpful as the device is supposed to be the size of a jet engine. If you are going to model at least try and get the closest starting point.
For example : a fast breeder reactor has a core ~~ 1 m^3 and needs liquid metal cooling and generates ~ the power in question.