Can he wear a cap lined with silk to protect his hair?
Question

I am a man and my hair is long. I want to keep my hair and scalp in good health always. Because it is winter here, I do not believe that I can go out without covering my head and my ears, but I know that winter caps are made of wool or cotton, which damage the hair, as they cause the hair to become thin and break, and I heard that it is good to line the woollen cap with satin or silk to keep the hair and scalp healthy, and satin is a fabric that is sometimes made of silk. Is it permissible for me to do that? I know that it is haraam for men to wear silk, but I read an answer on your website which says that those who are sick may be allowed to wear silk in order to reduce their suffering.
Praise be to Allah.Firstly: wearing natural silk is haram for men.
It is haram for men to wear natural silk, because of the report narrated by Abu Dawood (4057), an-Nasaa’i (5144) and Ibn Maajah (3595) from ‘Ali ibn Abi Taalib (may Allah be pleased with him), that the Prophet (blessings and peace of Allah be upon him) took a piece of silk in his right hand and  a piece of gold in his left and said, “These two are forbidden for the males of my ummah.”
Ahmad (6556) narrated from ‘Abdullah ibn ‘Amr ibn al-‘Aas from the Messenger of Allah (blessings and peace of Allah be upon him) that he said: “Whoever among my ummah wears gold and dies wearing it, Allah will forbid to him the gold of Paradise. Whoever among my ummah wears silk and dies wearing it, Allah will forbid to him the silk of Paradise.” Classed as saheeh by al-Arna’oot in Tahqeeq al-Musnad.
Secondly: wearing silk for the purpose of medical treatment is permissible
It is permissible to wear silk for the purpose of medical treatment, because of the reports narrated by al-Bukhaari (5839) and Muslim (2076) from Anas, who said: The Prophet (blessings and peace of Allah be upon him) granted a concession to az-Zubayr and ‘Abd ar-Rahmaan allowing them to wear silk, because of a skin disease that they had.
According to the version narrated by Muslim: … because of a skin disease that they had, or a sickness that they had.
Al-Haafiz Ibn Hajar said in Fath al-Baari: at-Tabari said: This indicates that the prohibition on wearing silk does not include one who has a sickness that may be alleviated by wearing silk. End quote.
To that may be added items that protect against heat or cold, when there is no alternative. End quote.
It says in Zaad al-Mustaqni‘: In the case of necessity, or a skin disease, or sickness, or lice.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said in his commentary: The words “or sickness” mean that it is permissible to wear silk if a person has a sickness that will be alleviated or cured by wearing silk. Reference concerning that should be made to doctors. If they say: If this man wears silk, he will recover from his sickness, or his sickness will be alleviated, then in that case he may wear it.
The words “or lice” mean: it is permissible to wear silk to get rid of the lice, because he may need that either for psychological reasons, because  he cannot bear to go out and meet people with lice on his clothes, or for physical reasons, because these lice bite him and cause annoyance, and silk – because it is so soft and clean – will repel the lice, because lice usually prefer a dirty environment." (Ash-Sharh al-Mumti‘  2/216).
You are not sick, praise be to Allah, so there is no concession allowing you to wear natural silk.
As for artificial silk, there is nothing wrong with wearing it.
So you should look at the satin. If it is made with natural silk, it is haram to wear it, but if it is artificial, then it is permissible to wear it.
And Allah knows best.