Praying without covering the head

on praying bearheaded (without a Turban or Kufi)

Shaikh Albaani (May Allaah's mercy be on him) (From Al-Qawl Al-mubin fi akhta' Al-musallin by Mashhur Hussain on page # 58 of the 2nd edition):  "Praying bareheaded is makruh (disliked)."

It is not established at all that the Messenger (sallallaahu 'alaihi wa sallam) ever prayed outside the pilgrimage with bare head, without a turban/cap. Whoever thinks he did so then he should bring the proof. If he (sallallaahu 'alaihi wa sallam) had done so, it would have been recorded. The narration attributed to Ibn 'Abbaas that the Prophet (sallAllaahu 'alayhi wa sallam) would sometimes remove his cap and place it as a sutrah in front of him is weak (da'eef). 

Shaikh Albaani (May Allaah's mercy be on him) (Al-Din al-khalis (3:214) and al-Ajwiba al-nafi`a `an al-masa'il al-waqi`a (p. 110): "All acknowledge that it is desirable for the Muslim to enter prayer in the most perfect Islaamic appearance, due to the hadeeth: "Allaah is worthier of your self- adornment" [hasan]. And it is not part of excellent attire in the custom of the Salaf to habitually bare one's head, and walk in that guise on the road and when entering places of worship. Rather, it is a foreign custom which infiltrated many Islaamic countries at the time the disbelievers invaded them and brought their habits with them. The Muslims began to imitate them in this, and they lost thereby their Islaamic personality as well as through other similar acts... Nor is it established that the Prophet ever prayed bareheaded and without a turban other than in the state of ihram, although there were plenty of occasions to report it if he did. Therefore, whoever claims that he did, let him produce the proof, for truth is more deserving to be followed."

Shaikh Albani (May Allaah's mercy be on him) goes on to explain the mistake of some brothers in Egypt who brought the proof of the permissibility to pray without covering the head by analogizing with how the head is uncovered for someone in ihraam during the pilgrimage. This is wrong since not covering the head during the pilgrimage is from the law (Sharee'ah) of Allaah. If their analogy was right then they should make it compulsory to pray without any head covering at all since it is obligatory to do so during the pilgrimage and to follow all the other restrictions of Ihraam in regular life! [Tamaam-ul-Minnah fee ta'leeq 'alaa fiqh-us- Sunnah by 'Allaamah Albaani] 

Allamah Jauzi (Allah's mercy be on him) (From Fatawa Rahimiyya 3:202 #308.): "To keep the head bare before the people is an act which is looked down upon and is against gentleness, humanness, etiquette, and gentlemanly decorum."

Hanbali Fiqh (Quoted By Ibn Qudama, al-Mughni (1994 ed.) 1:404-405): "It is mustahab to pray using a Thawb, Silwar (Sunnah pants) or a Izaar (loincloth) and a turban"

Maalik Fiqh (Quoted by Ibn Abi Zayd, al-Jami` fi al-sunan (1982 ed.) p. 228): Imaam Maalik said "The turban was worn from the beginning of Islaam and it did not cease being worn until our time. I did not see anyone among the People of Excellence except they wore the turban, such as Yahya ibn Sa`id, Rabi`a, and Ibn Hurmuz. I would see in Rabi`a's circle more than thirty men wearing turbans and I was one of them, and Rabi`a did not put it down until the Pleiades rose (i.e. until he slept) and he used to say: "I swear that I find it increases intelligence."

Shafi`i Fiqh (Quoted by Al-Misri in Reliance of the Traveller p # 122): "It is mustahab to pray using an ankle-length Thawb and a turban"

Hanafi Fiqh (Quoted by Al-Shurunbali in Muhammad Abul Quasem p #91): It is mustahab or praiseworthy to pray using "three of one's best clothes, a Thawb, Silwar (Sunnah pants), and turban or kufi" According to the Hanafi school (Al-Jazayri, al-Fiqh `ala al-madhahib al-arba`a, Kitab al- Salat p. 280-28) [among] the disliked acts (al-makruhat) in prayer are:... i`tijar, which is to tie a scarf around the head and leave the center bare;... [or] praying bareheaded out of laziness. As for praying bareheaded out of humility and submission, it is permitted (ja'iz) and not disliked.(16)

Shaikh `Abd al-Qadir Jilani (From Ghunyat al-talibin 1:14)
"It is the method or habit of orthodox or civilized virtuous men to keep the head covered."

Few Sahih Hadeeth on covering the head with a Kufi (cap) or Imaamah (Turban) being Sunnah.

Sahih Al-Bukhari Volume #1 pg#536: Ibn Abbas (RadhiAllaahu Ánhu) reports that Rasulullaah (SallAllaahu Álayhi Wa sallam) addresses the Sahâbah while wearing a black turban.

Tabrani And Imaam Suyuti: Ibn Umar (RadhiAllaahu Ánhu) narrates that Rasulullaah (SallAllaahu Álayhi Wa sallam) used to wear a white cap (kufi). Tabrani has reported this hadeeth to be Hasan (reliable) and Suyuti has classified this hadeeth as highly authentic (Sahih) in the book Sirajul Muneer vol #4 pg#112)

Abu Dawood and Tirmidhi
Roknah (Radhiallaahu Ánhu) reports that Rasulullaah (SallAllaahu Álayhi Wa sallam) said "The distinction between us and the polytheists is the turbans over our caps." Also quoted by Al-Tabrizi in his Mishkat Al-Masabih and this clears up the false notion that this was just the way of the Arabs and not a particular practice of Rasulullaah (SAW) and this shows us that we should wear caps under our Imaamah's to differentiate from the Sikhs and other Kuffaar who wear turbans but without caps under them.

Understanding of Sahabah (RAA) in following Rasulullaah (SAW) in wearing Turbans and kufis (Caps)

Sahih Al-Bukhari Volume 2 pg #863
It is mentioned that Anas Bin Malik (RadhiAllaahu Ánhu) used to wear a kufi (cap).

Sunan Abu Dawood Book 3, Hadeeth # 0948:
Narrated Umm Qays bint Mihsan: Hilal ibn Yasaf said: I came to ar-Raqqah (a place in Syria). One of my companions said to me: Do you want to see any of the Companions of the Prophet (SallAllaahu Álayhi Wa sallam)? I said: A good opportunity. So we went to Wabisah.  I said to my friend: Let us first see his mode of living. He had a cap (kufi).