I ran a K6-2 350 w/o a fan for a long time without even realizing it...but I don't recommend that.
The K6-2 500 disperses about 20.75 watts of heat.
If you got an SK-7 for $25 and a quiet fan, and undervolted the fan to 5v, the processor would be very cool, and would be dead silent. I recommend the SK-7 because it is quite possibly the cheapest all-copper heatsink that fits an 80mm fan. You could probably run the processor with the SK-7 without a fan, but unless your board has temp. monitoring, it's not a great idea.
Before you run off and do that, make sure the Socket 7 and Socket 370/A have the same clip configs. I can't remember if they do...
Socket 7/370/462 all have the same socket dimensions, but the older Socket 7 mobo's may have capacitors really close to the socket. My old Aopen AX59 pro, for example. has the end lug on each side missing 'cuz there's a cap butt up against it.