Answer

Personally, I do not see why one should ascend. But if you are going up anyway:
Rabbi Azaria Ariel
Immersion on Tisha B'Av for the purpose of ascending the Temple Mount
Question
How can one immerse and prepare for ascending the Temple Mount on Tisha B'Av?
Thank you
Answer
To the questioner, greetings!
It is permitted to immerse on Tisha B'Av for the purpose of ascending the Temple Mount, as emerges from the Shulchan Arukh, Orach Chayim 613:11-12, and the Bi'ur Halakhah there, s.v. "in our time": when immersion is necessary for purification, it is permitted even on Tisha B'Av and Yom Kippur. The immersion of someone who experienced a seminal emission for prayer is not a strict legal requirement, and likewise a woman's immersion to become permitted to her husband is not necessary on Tisha B'Av and Yom Kippur, and therefore these do not override the prohibition of washing. But immersion that is required by law—even though there is no obligation to do it specifically on that day, but it is needed for that day—is permitted. So too ruled my uncle, Rabbi Yaakov Ariel, may he live long, in Be'ohalah Shel Torah, vol. 4, sec. 23, that it is permitted to immerse on Tisha B'Av for the purpose of ascending the Temple Mount; and in a spoken conversation he told me that the same applies to Yom Kippur.
For further expansion on the topic, see the book Sha'arei Heikhal on tractate Yoma, section 191.
Another possibility is immersion on the eve of Tisha B'Av. Although it is customary to immerse as close as possible to the ascent to the Mount, strictly speaking immersion from the previous day is also effective, provided there is no sign of a seminal emission during the night.
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