Percival P. Cassidy wrote:

It's a looong time since I bought an Intel CPU. I just ordered a CPU and
mobo, and now I'm wondering whether I should have ordered heat sink
compound/thermal grease as well.

In a retail package for an Intel CPU, the included HSF will already have
pre-applied thermal tape. It is for one-use only. If you ever remove
the HSF, clean it and the CPU with isopropyl alcohol and apply a new
thin transparent layer of thermal paste. Don't touch the thermal tape
with your fingers that would pollute it with your body oils. You might
want to use isopropyl alcohol with a cotton ear swab to clean the CPU
plate before mounting the HSF to it, especially if you weren't careful
in handling the CPU.

I always order some thermal paste along with a CPU and/or HSF order if I
don't have some on hand. That's in case I need to remove the HSF
because temperatures are too high which could be due to an imperfect
mounting of the HSF or CPU. Tape should only be used once. In fact,
paste should only be used once, too. If you ever have to remove and
remount the HSF, use new paste.