@Hyperspeed
The 060 was designed not to require any cooling, and mine never got too hot to touch without a heatsink. I'd say it got as far as "warm" and stayed there... You got it clocked? Or maybe a voltage regulation issue? What model board is it on? Mine's on a DCE Blizzard. I'm thinking that maybe an older revision of the chip, or lower performance glue logic could be causing it to generate more heat.
Mine's now run at 66MHz for 4 years or so, no problems. When I clocked it it did get too hot to touch, so I put a 486 cooling fan on it, secured it with some "hi-tech" cable ties and heatsink paste, and now it's positively cool to the touch, can't be more than 25 degrees C. Such a fan will cost ya less than €10, and will usually have a pass-through for a drive power connector, so is very easy to fit.
Unless you have a custom modified tower, then you may have to cut a hole in the side of it for the fan (like me!) :-o