Question 112: What is the wisdom and narrations of placing the Holy Qur’an on top of your head? When are the appropriate times during the year to do this?
Answer 112: As we Shia follow the traditions of the Infallibles (as), we all follow whatever they have been told us in this regards.
Ali bin Yaqteen narrated from Imam Kadhim (as) that the Imam (as) said: “Take the holy Quran in your hand and place it on top of your head and then say:
اللَّهُمَّ بِحَقِّ مَنْ أَرْسَلْتَهُ إِلَى خَلْقِكَ وَ بِكُلِّ آيَةٍ هِيَ فِيهِ وَ بِحَقِّ كُلِّ مُؤْمِنٍ مَدَحْتَهُ فِيهِ وَ بِحَقِّهِ عَلَيْكَ وَ لَا أَحَدَ أَعْرَفُ بِحَقِّهِ مِنْكَ يَا سَيِّدِي يَا سَيِّدِي يَا سَيِّدِي
Then say “یا الله” (O Allah) for ten times, “بحق محمد” (by the right of Muhammad (pbuh)) ten times, and then continue saying each name of the Infallible Imams (pbuth) ten times. After all has been mentioned ten times, beg Allah whatever you want. So, Allah, the Almighty will grant all your wishes.
It is said (in traditional resources) that whenever you face any problems try to offer two Rakats, place the holy Quran on top of your head and mention the name of Allah (SWT), Holy Prophet (pbuh) and ahlul bayt (pbuth) ten times, so Allah. The Almighty will grant your wishes. 
While placing the qur’an on the head. Remind yourself that true salvation can only be achieved by always keeping the rules of qur’an ahead of us to follow. The fact that we put the Qur’an on our head is a sign of respect and reverence. We beseech Allah by the thaqalayn – the speaking and the silent Qur’an. Pray for Aql/Intelligence to be Kamil (complete), it is Kashe (submits) to quran & acquires Noor (light) from it.
O Allah! I appeal to Thee in the name of this Qur’an and the Rooh that was sent along with it, and in the name of the Momin (believer) whose praise is contained in this Book and The obligation that is on them. No one else recognizes the right and truth more than Thee
“Allaahumma be haqqe haazal Qur’an we be haqqe man arsaltahoo beh, Wa be haqqe kulle momenin madahtahoo feeh, we be haqqeka alaihim fa-laa ahada a’arafo be haqqeka mink”
Note: There are no restrictions limiting the times of placing the holy Quran on top of our head. However, it is more recommended to do so during these holy Nights of Power (19th, 21st or 23rd or 27th night of Ramadan / or 15th night of Shaban).
For further information in this regards, please refer to the following answer:
Index: The sign of Laylatul Qadr, the Night of Power, answer 065.
Index: Definition of Dua, Means and Intercession, answer 148.
Index: Reciting Dua or Dikr in any language during the Prayer, answer 579.
 . Sheikh Hurr Ameli, Wasail al-Shia, Vol. 8, Pgs. 125-126; Sayid bin Tawoos, Radhi al-Din Ali, al- Al-Iqbāl bi l-aʿmāl al-hasanah, Vol. 1, Pg. 186-187.
 . Holy Qur’an (39:56).
 .Refer to: http://duas.org/.