Carbon Fiber fabrication FTW
if you really wanted to win you could use Carbon Nano Tubes and build a case that is also the heatsink
CNT have the same thermal conductivity as CBN and natural Diamond (2400w/m-K) about 6x better than Copper or Silver. Dont forget to use Graphene as your TIM and remove the CPU IHS to reduce overall system weight!
I hope yall have some friends at MIT