Use any that would fit. CPU TDP is very low and you can use sticky thermal pad instead of thermal paste.

If you use glue, you can attach a heatsink of any size you wish.

Personally I'll never glue a heatsink onto a vintage CPU, because I don't want to ruin the silkscreen.
It's just too bad that there weren't any widely available kits to attach removeable heatsinks to 386 class CPUs.
I think it might be possible for somebody to design one though. We just need a 3D printed plastic bracket, and a metal retention clip. The aluminium heatsink can easily be cut to size.

If you want to go the glue route, there are ways to do it without causing too much damage. Use thermal paste in the center of the CPU, and just a very small amount of glue at the corners.

Yes, the 486DLC gets a bit hot at times.
Back in time, I added a little heatsink, some thermal paste and a tiny bit of hot glue at the edge of CPU/heatsink.
In combination with the paste, it sticked just about enough.
I was using a desktop case, though. So the motherboard way laying down, not standing.

Alternatively, there are CPU heatsinks with a sticky thermal pad.
Removing such a heath sink could bs tricky perhaps.
Instead of using force, the heat sink must be rotated back and forth a bit to loose the adhesive?

Some normal thermal pads should have enough stickiness to hold small cooler in place.

Niborius wrote on 2022-04-24, 17:32:

I've got a motherboard with a TX486DLC/E processor on it. I did some research and from what I understand, a heatsink is highly recommended, and a fan would be even better.

My question is, how would I find a heatsink/fan for such an old model?
Is it really unwise to use the PC without any form of CPU cooling?

Unwise? Yes. The CPU will get hot (up to some 65-70C in free air for 40MHz version, more in closed case) otherwise. It will still work but at these temperatures degradation will happen faster - why risk what is now hard to find CPU dying if it can be prevented. You can do some testing for an hour or two but I would not recommend using such system long-term. Also the thermal cycling will stress the mobo and nearby parts (and solder joints) as well.

I mostly use small (35x35x10 mm) passive heatsinks, sometimes with a fan if there is space for it and the CPU is too far from the PSU to get any airflow, and silicon grease - cheap, non-toxic, non-conductive electrically (in fact a decent insulator), not active chemically, transparent. Can be pretty easily removed with a piece of cloth or paper towel. Does not dry out and harden (well, not that I've seen in years of usage). But it will "flow" more in temperatures above 40C or so, will not hold the heatsink in place on it's own. For that I tie 2 or 3 strong cotton strings around the CPU and the heatsink, works well enough. Easily removable.

For more permanent installs a thermal sticky tape (double-sided) does the job. If you don't want to risk the CPU markings getting damaged during removal (the tape sticks very well) then soak the thing overnight in 99%+ IPA. Or acetone if IPA doesn't cut it - this is much more aggresive chemical but these CPUs are sealed, nothing there the acteone could damage. Obviously any stickers would also peel off, same with IPA.

A heatsink alone will drop the CPU temp by about 10-15C, depending on size and amount of airflow it sees from PSU. If you need more cooling then a fan, even a slow one like 12V model running from 5V rail, or 7V (plugged between 12 and 5) will do nicely. In fact the fan doesn't need to be on the CPU, just nearby.