The Torah Portion of Pinchas is read during the Three Weeks (except during a leap year). Though there is no connection with this Portion and the period for the mourning over the destruction of the Bet HaMikdash, there is one passage that may be relevant. Hashem always spares the Jewish people.
Pinchas was rewarded by Hashem for having stopped the Bnei Israel from transgressing with the Moabites. In doing so, Hashem says: וְלֹא כִלִּיתִי אֶת בְּנֵי יִשְׂרָאֵל בְּקִנְאָתִי, “…and I did not wipe out the Children of Israel in my vengeance.” (Num. 25,11) Because of his action the Bnei Israel were spared. Similarly, when Hashem destroyed the Bet HaMikdash, according to the Midrash, Hashem destroyed the stones of the Temple but spared the Jewish people.
The Maharal of Prague, who lived in the 16th century, makes a very remarkable observation. He explains, we are told the Bet HaMikdash was destroyed because of unfounded hatred. The Maharal indicates that before the Temple was built Jews were permitted to offer sacrifices on any individual altar. The Bet HaMikdash was built to unite the people and thereafter the private altars were no longer permitted. When the people were not united and were divided with petty hatreds, the Temple no longer served its purpose and was destroyed.
Rabbi Simcha Bunim makes another observation. He says when the Jewish people reach the moment when they can endure the Galut and do not use all means to bring about the salvation, then that leaves no other option except that Hashem Himself must bring about the redemption.