A Dome of the Rock location for the Temple would have made it impossible to supply running water to the Temple.

 According to the Mishnah, the way that blood was washed from the floor of  the Priest's Court where sacrifices were performed was to open the floodgate of the aqueduct directly into the court .
 

The Jerusalem Water Aqueduct

The water canals that supplied Jerusalem began in the area of the Hebron mountains, passed through the Solomon's Pools near Bethlehem, and flowed to Jerusalem. The lowest canal reached the Temple Mount through the Jewish Quarter and the Wilson Bridge. According to the ancient authorities, the water conduit supplied water to the High Priests' mikveh (ritual bath) located above the Water Gate, and it also supplied water for the rinsing of the blood off the Azarah (Priests court). Portions of this aqueduct are plainly visible to this day.

"Living water," that is fresh, flowing water, not water from a cistern was required for the ritual bath (mikveh) used by the temple priests, and for the washings of the temple in connection with the sacrifices.

A survey of the level of the aqueduct reveals that if the Temple had been located at the same elevation as the present Dome of the Rock shrine, the aqueduct would be  too low to serve either the Azarah or the Water Gate. From this survey, it appears that the Temple must have been 20 meters lower.....
.-Lambert Dolphin- http://www.templemount.org/theories2.html
(Note: a meter equals 39.37 inches making it 65 feet below the present level of the mounts surface in the southern area)

Part of the aqueduct is still in existence. . In fact, remains of the aqueduct itself show that after entering the Temple Mount across Wilson's Arch, it turned to the southeast towards the Al Aksa fountain and its associated cisterns.
 

The tunnels which exist today, leading from the Double and Triple Gates, are arched constructions from a later period and we can not assume that at the time of the Second Temple there were such tunnels. According to the descriptions in the literature, it seems that people gained entrance directly to the temple court area coming up from the City of David, through the Huldah and Ciponus Gates directly into the temple courts without traversing intervening tunnels behind the gates (which tunnels are there today).  This means that if the Double and Triple Gates (+725 meters above sea level) are the Huldah Gate, and the Barclay Gate (+725 m) is the Ciponus Gate, then the level of these three gates is at the original level of the Temple Mount and we have to lower the level of the Temple Mount by at least 11 to 16 meters from the currently existing court level (+737 meters above sea level).

Information Source from
http://www.solomonstemple.com