Tamuz is a month where many tragedies happened to Klal Yisroel, such as the 17th of Tamuz, with all its related tragedies. Tammuz we also know is one of the summer months where the Yetzer Hora works extra hard to trip us up. One fascinating allusion to this idea, from the Chida in the name of Reb Shimshon Ostropolier, was already written up in a previous post on Shmiras Einayim. (See there, third section "Yetzer Hora Is Stronger in the Summer"). We all know Shmiras Einayim is, understandably, much more difficult in the summer and interestingly the sforim mention many more relationships between the month of Tammuz and the eyes.
The Summer Months Represent the Eyes
The Bnei Yisaschor says that according to the Arizal each month represents another part of the head. Tammuz represents the right eye and Av the left eye. An allusion to this is in Eicha (1, 16) עֵינִי עֵינִי יֹרְדָה מַּיִם and the Gemara in Tanis (24) says a kallah, meaning Klal Yisroel, whose eyes are nice; you don't have to check her whole body (to see if she's healthy) and the opposite is also true – if her eyes are not nice than…. We see here a fascinating allusion – if Klal Yisroel (who's called a kallah) guards their eyes than the rest will stay pure. (For more on this, see Bnei Yisaschor, Tammuz Av 1:4)
Satan's Wife & the Antidote
Each one of the twelve months represents one of the twelve possible permutations of Divine Name, Yud-Kei-Vav-Kei. The Minchas Elazar in Shaar Yisaschor points out that the permutation for Tamuz is completely backwards from the normal spelling - it is written ה-ו-ה-י. This name comes from the last letters of the words from Megilas Esther (5, 13) זֶ׳ה אֵינֶנּ׳וּ שֹׁוֶ׳ה ל׳ִי. The gematria of this posuk is 480, equal to that of לילי״ת (Satan's wife), another allusion to her extra strength in this month. Also, Haman was the one who said the words in this posuk, and he descends from Esav, who has power over the month of Tamuz.
That's why there were 480 Batei Medrashim in Yerushalyim, to counteract the power of לילי״ת.(The Seforim Hakedoshim teach that something with the same gematria has the power to counteract the other) The Rambam writes at the end of Hilchos Isurei Biah that the Yetzer Hora only rules over a heart that is bereft of Torah. Therefore immersing oneself in Torah is the way to win over this Yetzer Hora. Interestingly, Likutei Mohoran 214 mentions that the gematria of לילי״ת is equal to that of תלמוד, alluding that if one learns Torah properly he can overpower the Satan, but if one doesn't learn properly than chas v'sholom the opposite can happen.
Remember the Torah of Moshe
The previous paragraph is a great segue into the following from Likutei Mohoran 217: The first letters of זִ׳כְרוּ תּ׳וֹרַת מֹ׳שֶׁה(Malachi 3, 22) (Remember the Torah of Moshe) spells תמז without the letter "ו". We need the remembering of the Torah to fix the forgetting of the Torah, which came about through the breaking of the luchos in the month of Tammuz. The Gemara in Eruvin (74) says that if the first luchos would not have been broken, Torah would never have been forgotten from Yisroel. Therefore Tammuz is without a "vav", because the luchos were the bechina of "vav", as the Gemara in Baba Basra (14) says that the luchos measured 6 tefachim long and 6 tefachim wide. Also, the first letters of ז׳מן מ׳תן ת׳ורתנו spell תמז, because this was the month when we received the luchos. It is again missing the letter "ו" because the luchos, which are the bechina of "vav", were broken, as mention previously.
A Segula for Shmiras Einayim
Sefer Hamidos (Re'iyah #9) says that when a man goes out to the market and is worried that he might come to hirhurim through his seeing beautiful women he should say the posuk: (Yeshaya 33, 7) הֵן אֶרְאֶלָּם צָעֲקוּ חֻצָה מַלְאֲכֵי שָׁלוֹם מַר יִבְכָּיוּן
See Shmiras Einayim - Thoughts, Stories and Segulas for much more on the subject of Shmiras Einayim.