If the Hurva is rebuilt for a second time, the construction of the Third Temple will begin...

 

 If anyone wonders why Palestinians and Arabs in general are so suspicious of Isareli intentions after the reopening of the 'Hurva synagogue',  it is useful to read the following (from a blog Destination Yisra'el:

 Jewish Expectations that Construction will begin on the Third Temple in the Spring, 2010

The New Hurva Synagogue in Jerusalem completing Construction

According to a centuries-old rabbinical prophecy that appears to be coming true, on March 16, 2010, Israel will begin construction of the Third Temple in Jerusalem. During the 18^th century, the Vilna Gaon, a respected rabbinical authority, prophesied that the Hurva Synagogue in Jerusalem, which was built during his day, would be destroyed and rebuilt twice, and that when the Hurva was completed for the third time, construction on the Third Temple would begin.

The Hurva Synagogue was first destroyed shortly after its initial construction when Muslims demanding the return of loans tore it down. The synagogue was rebuilt a hundred years later and became the most important Jewish house of worship in the Holy Land, only be blown to pieces by Jordanian troops during Israel’s 1948 War of Independence.

Or, if that not convincing enough, this article from Haaretz 30.11.09

If the 18th-century rabbinic authority the Vilna Gaon was right, on March 16, 2010, construction will begin on the third Temple. His projection states that the auspicious day will coincide with the third completion of the Hurva Synagogue in Jerusalem's Jewish Quarter.
The great day is at hand: On March 15, the reconstructed Hurva Synagogue, considered the most important house of prayer in Jerusalem will be rededicated. It was last destroyed in the War of Independence.