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.