I spread a thin layer of the compound as instructed here. After putting it back together I went from the yellow light of death, to the PlayStation overheating within 30 seconds. I then disassembled, and instead of spreading a thin layer once more, I applied a pea-sized dab of the compound in the middle of each chip. I then reassembled without spreading the compound. The PlayStation now runs with no issues.
I read on several forums that the compound will spread on its own through heat and the reassemble of the components.