Roman numerals use I's, not ones... Please use PIII or P3 so we know what the hell you're talking about ;P
Anyway, some didn't have fans on the heat sink themselfs, but ones near by. An old IBM I have has this duct going off the power supply and blows directly on the processor. I've seen others that had fans basically laying on top of the HS and were just removed to gain access(Gateways I think...)
If the HS is good, you can run it for a while without a fan, but they will over heat. I know my video computer tends to(using that processor from the IBM)