Question Summary:
1) If a Musalli gave Adhan without wearing a topi (headgear), is the Adhan valid? 2) What is the status of covering the head while giving Adhan?

Question Detail:

1)     If a Musalli gave Adhan without wearing a topi (headgear), is the Adhan valid?
2)     What is the status of covering the head while giving Adhan?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
1)     If a musalli gives Adhan without a topi (headgear), the Adhan is valid.[1]
 
2)     The wearing of the topi is a sunnah of Rasulullah Salallahu Alayhi Wa Sallam and his companions Radiallahu Anhum .It is also the dressing of the pious. For more details on the topi and its emphasized importance with academic references, you may refer to THE CROWN OF A BELIVER by Mufti Husain Kadodia (Damat Barakatuhu) which is also available in PDF form.
And Allah Ta’āla Knows Best
Ismail Dawoodjee
Student Darul Iftaa
Zambia
Checked and Approved by,
Mufti Ebrahim Desai.
www.daruliftaa.net 
[1] ذكر منلا مسكين عند قول المصنف في مسائل شتى آخر الكتاب، ولا بأس بلبس القلانس لفظ الجمع يشمل قلنسوة الحرير والذهب والفضة والكرباس والسواد والحمرة اهـ والظاهر أن المعتمد ما هنا لذكره في محله صريحا لا أخذا من العموم (در المختار ج6 ص755 سعيد)