Wikipedia http://en.wikipedia.org/wiki/Dome_of_the_Rock#Accessibility :

----

Until the mid-nineteenth century, non-Muslims were barred from the area. Since 1967, non-Muslims have been allowed some entry, but non-Muslim prayers on the Temple Mount are not allowed.

After Ariel Sharon, then Israeli opposition leader, visited the Temple Mount in 2000, in what was considered as a provocative gesture that set off Muslim rioting, non-Muslims were forbidden to enter the Temple compound.

In 2006, the compound was reopened to non-Muslim visitors free of charge, between 7:30-11:30 a.m. and 1:30-2:30 p.m. during Summer and 7:30-10:30 a.m. and 1:30-2:30 p.m. during Winter. However, timings can vary depending on the date and it is highly recommended to arrive early. Non-Muslims may never enter on Fridays, Saturdays, or Muslim holidays. Entry is through a covered wooden walkway next to the security entrance to the Western Wall known as the Mugrabi or Maimonides Gate. Entry to the mosques themselves is prohibited to non-Muslims, as is access to the Temple Mount through the Cotton Market. Visitors undergo strict security screening, and items such as Hebrew prayerbooks or musical instruments are not allowed.

Some Orthodox rabbis regard the rules of entry to the compound established by the Muslim Council as a violation of Jewish law. This is based on the belief that since the time the Temple was destroyed, centuries ago, the precise location of the Holy of Holies, the sanctuary entered only by the High Priest, is not known. Hence a restriction applies to the entire compound. However, other rabbis believe that modern archeological and other evidence has enabled them to identify areas that can be safely entered without violating Jewish law.

----

So you're right to say that non-Muslim prayers are not allowed on the Temple Mount.