More weird news:
I e-mailed HP, and what they said,
"This is with reference to your e-mail regarding the heat sink of the processor of your Evo D510 Ultra-Slim Desktop PC.
Please note that the heat sink can not be installed in the PC as the processor and its heat sink fan are not a separable part. Therefore, you can not buy a heat sink/fan for this unit.
However, you could buy the following processor assembly for this unit which consist processor with heat sink."
Sounds like they are just trying to get me to buy one of their processors.