As the Talmud instructs (or here, the talk on October 4, 2008 source notes):
Amen’ is not made use of in the Temple.6 And whence can it be adduced that the response, Amen, was not made use of in the Temple? — For it is said, Stand up and bless the Lord your God from everlasting to everlasting; and let them say: Blessed be Thy glorious Name, that is exalted above all blessing and praise...What them was said in the Temple? Blessed be the Lord God, the God of Israel, from everlasting to everlasting. Blessed art Thou who redeems Israel; and the congregation respond, Blessed be the name of his glorious kingdom for ever and ever
Today, I participated in the Mincha (Afternoon) service at the Rav Goren Synagogue as I did two years ago.
In accordance with the above instruction as to the text to be uttered, this video will provide you with the audio for that text as the synagogue is located inside the space of the Temple Mount:
And here are some snapshots of the day's activities:
On Rechov Haguy Street, opposite the memorial plaque commemorating the murder by stabbing of Elchanan Atali, there's an alleyway:
and that alleyway has a sign, in Hebrew, pointing to the "Little Wall"
and there, just before you would enter the Temple Mount, you turn left and walk into a courtyard (here's how it looks coming back out):
and you will come upon a section of the Western Wall north of the Western Wall Plaza:
Afterwards, I continued to the Rav Goren Synagogue.
Here, the Sefer Torah is being held aloft at the end of the reading:
another view of the congregation:
a view through the reinforced windows of the Dome of the Rock:
The sign warning that you are about to cross over the Western Wall towards the east and will be entering the Temple Mount sanctity (the synagogue: is actually on the second floor of a building that abuts into the compound over columns along the Western Wall):