I was pretty sure none of the 486 CPUs absolutely required a cooling fan (though I only had a DX2/66MHz): I remember Pentium II being the first CPU I've seen that absolutely required it (came with one integrated on the second computer I assembled for myself), and I distinctly remember having trouble testing an AMD CPU a year of so later on a computer I was assembling for someone else because... well, it wouldn't even POST without a CPU cooler.

Luckily I did not fry it and after adding a cooler it worked just fine.

I don't remember if AMD or Cyrix CPUs were worse though.