The First and Second Holy Temples were both destroyed on the 9th day of the Hebrew month of Menachem Av (three weeks from the 17th of Tammuz when the invaders breached the wall of Jerusalem). The preceding three weeks are a period during which Jews mourn this loss, and fervently pray for the Third Temple that will be established by the Messiah from the dynasty of King David, speedily in our days.
A Noahide is not required to fast on the 17th of Tammuz or the 9th of Menachem Av. Nevertheless Noahides may and should give charity during not only these 2 days but during the 3 weeks altogether in order to awaken Divine compassion.
You may help other Noahides here: http://worldnoahidecommunity.org/?page_id=8138