During prayer our beloved prophet Muhamamd swah head was covered all the time. Weather it was headcap or not is something I don't know. Sorry for that. But if possible always cover your head during Salah. Even if you don't cover your head you Salah will be complete but try to improve on your Salah by covering your head.
Well you have to cover yourself (and your head) while you are praying but if you're not praying but you are in the house, you don't have to cover your head. Unless there are men who are not blood relative in there. Dahlia Nasir
Head for cover.
Must dress correctly (cover head) and must not wear perfume. Otherwise they are welcome to come.
1. A head-covering such as a kippah or hat 2. Tallit (prayer-shawl) 3. Tefillin (phylacteries) The Tallit and Tefillin are worn only during the morning services.
The only difference between prayer for a man and a woman is that a woman must cover everything exept her face and hands, and man must cover everything from his navel to his knees (although it's better if he also wears a shirt and and head covering.)
Islams wore silk head things along with their dress or pants
Religious Jewish males, and married females, cover their heads at all times. Many others do so at least during prayers. The kippah is worn to serve as the head covering. Covering one's head signifies awareness that God is above. The Tallit is a symbol of being enveloped in prayer.
Head for cover.
Hindus cover their heads while praying or chanting mantras. This is done out of respect and because it is a Hindu belief that energy is lost from the top of the head. Covering the head helps to maintain the energy derived from chanting.
yamaka (not sure of the spelling). It's the article Jewish men wear on their head during synagogue and prayer.
"Tefilin" (see a dictionary). One worn on the head, another worn on the arm, during morning prayer,every day except Sabbath and holidays, beginningat Bar Mitzvah.