Here are some relevant examples (including newer hotter chips) from my recent experience:
Someone just gave me a Leading Edge Winpro 486. It has a TI 486SLC/E CPU which has no heat sink or fan. There is no space or provision for either, so I assume it has been running like this for years.
I have a 486DX4-S/100 which does not have a fan. I don't want to open it up right now to see if it has a heat sink, but it might not.
I have a Pentium 60 gold top which runs hot without a fan. However a little fan and no heat sink works. I'm not even sure that it wouldn't be OK without the fan - I just didn't like it so hot.
I have recently run a Pentium Pro without either heat sink or fan, but I deliberately underclocked it for the purpose.
I run a Pentium 133 with only a heat sink. It has a fan, but I disconnected it to make the machine more quiet. This machine runs
24/7 without any problem whatsoever. I left the fan in place just in case I needed it in hot weather, but the need has never arisen.
Looking at my "old board inventory", some 486s have a heatsink, some have heatsink and fan, and some have none. Years ago I used to run a 486DX2-66 without a fan. In those days I had other 486 machines too, and never did I have such fancy equipment as a CPU fan - IIRC, those were just starting to come out then.
Presumably it depends a lot on how you drive them, as witnessed by my running a PPro w/o either heatsink or fan. Some cooling technology should probably be filed under "artistic enhancement".
To me it looks like your answer is "
semi optional" just like you said.