Just had a dark Power Pro 550 PSU die on me at 4 yrs old, out of warranty so dumping it, but have taken out the fan to use as a case fan.
But puzzled by how to connect it up to my motherboard, or a cable connector.
Some details.

Motherboard Gigabyte 970A-DS3
Case Antec Solo ( original not MKII)
PSU Silver Power SP-S460FL

Fan from the old PSU is a Protechnic Electric MGT12012LR-A25 and has two pairs of wires, one pair that led out of the PSU for remote (motherboard?) connection, this is a white and black pair which terminates in a 3 pin connector with the cables going to the outer two pinholes
The second pair is internal to the PSU and I assume is where it got power from,this pair is red and black and ends in a 2 pin connector, and being for use within the PSU is of course a very short lead so I will have to extend this anyway.
I need help to understand how I might connect up this fan, I know its 12 volt and probably has ability to respond to temperature but do not want to just try connecting up without advice.
Any info welcome!

This should explain it: http://www.allpinouts.org/index.php/Motherboard_%28CPU%29_3_Pin_Fan_Connector (they obviously cocked up the colours in the first picture; compare to any 3-pin case fan)

Pin 3 is the RPM signal, from your description this is the one going to your mobo right now (with Black ground wire for some reason; should not be necessary). The shorter pair is no doubt the power lead and its ground as you suspected.

Buy a 3-pin connector, some extra wire(s) and plug the wires as seen in the link and you should be good to go!

PS. More than likely the temperature control is not built into the fan, wouldn't make sense cost wise. You CAN take a peek to see if there is something like a sensor at or near the hub of course.

Thanks for that info and link, I will set it up as a 3 wire fan when I have a bit more time. For now I have spliced the power and ground pair to a spare length of cable with a 3 pin connector, that just has two wires, plugged it into a four pin chassis fan socket on the motherboard. Works fine, fairly slow turning but moves a good amount of air so am happy with that. and it is silent, which is what I was hoping.
Having to think hard about setting up the case fans with this new fanless PSU.
I have a 120mm at the rear blowing out, level with the Arctic Cooling 7 pro V2 so helping the air away from that, and this newest one I have mounted at the front bottom of the case, blowing in.. Not sure how any air is going to be pushed into or pushed out of the PSU yet....Its not a hot running build so hopefully it will be OK as it is.