No answers, but suggestions.
Check to see if your library has any Heat transport books.
There are quite a few equations for heat transfer via fins, different materials. etc.
I dont have my book on me, otherwise id be happy to give you the necessary thermal conductivities, other constants, and equations.
Edit: If you intend to calculate heat dissapated from the heatsink, you will quickly realize that you have a ton of calculations to make - ie. radiation from fins, natural convection, forced convection if any, on top of the conduction.
This essay will probably be one of heat transport, not thermodynamics.
Perhaps an essay on water cooling a CPU would be a combination of heat transport and thermodynamics. Especially when you describe the pump, resevoir, heat blocks, tubing, radiators. This is pretty much an "outta the book" prime example of a thermodyamic process. It would get involved quickly however - explaination on imporance of size of tubing, pump's power, pressure head, efficiency of radiator, efficiency of pump, etc.