There are 2 hard drives and one of them is overheating badly.
I've done some prelim searches, but am very confused about what to buy.
I guess I need a fan or fans, but do I need a fan controller?
Not necessarily... if you buy fans that are too fast and loud you
might WANT one, but you don't "need" it.
Some sites give compatibility info, but most don't. Is this essential?
Compatibility info means what exactly?
You need fan(s) of proper dimensions, mounting ears that accept
the attachment method your case uses (typically plastic cage or
metal screws), and a plug compatible with your needs, whether
that be a 3-pin connector for an unused motherboard fan header
(and fan wire/leads long enough to reach that header), a molex
4-pin connector to connect directly to the power supply, OR an
extension cable with or without adapter function to convert
between the 3-pin motherboard and 4-pin molex type of connectors.
http://www.svc.com has very low prices on such extension and
adapter cables and very low shipping if only small items like t
his can be shipping regular USPS ground (but that takes 2-3 weeks
to arrive).
The 2 drives are in the 2nd and 3rd slot (bay?) from the bottom.
The system is Athlon.
If the drives are stacked one atop the other then lack of airflow
can make one (or both) drives overheat somewhat even with a
fan... ideally there should be at least 1 cm inbetween the drives
for airflow, and either a fan in front of them (front meaning
front-side of case) to push air though, or large holes in metal
wall of case so rear fans can pull air in though this passive
intake, still pulling air though the gap between the drives.
If your case doesn't allow space between the drives you might
consider a 5 1/4" bay mounting. Suitable hard drive coolers and
mounting brackets are available or use the old traditional metal
rails that screw to the sides and a front faceplate cover that
allows air to be drawn in.