Shama-il Tirmidhi Chapter 006, Hadith Number 001 (044).
Abu Rimthah Taymi Radhiallahu 'Anhu says: "I attended a gathering of Rasulullah Sallallahu 'Alayhi Wasallam with my son. Rasulullah Sallallahu 'Alayhi Wasallam asked me, 'Is this your son?' I replied: 'Yes, this is my son. You be a witness to it.' Rasulullah Sallallahu 'Alahi Wasallam said: 'The revenge of his crime (jinayah) is not on you, nor is the revenge of your crime on him.' (This will be explained in the commentary). Abu Rimthah Radhiallahu 'Anhu says: 'At that time I noticed a few hair of Rasulullah Salallahu 'Alayhi Wasallam were red." Imam Tirmidhi says: "This hadith is the most correct and closest on the subject of using a dye."
It was the custom in the pre-Islamic times (jaahiliyah) that a son was punished for the crimes of his father. On this basis Abu Rimthah Radhiallahy 'Anhu said this, so that if it would be necessary at any time, Sayyidina Rasulullah Sallallhu 'Alayhi Wasallam would be witness that truly this was his son. Sayyidin Rasullulah Sallallhu 'Alayhi Wasallam in refuting this custom of the jaahiliyyah said: 'This is not the law of Islaam, that one person commits a crime and another gets punished for it." (No laden soul can bear anothers load. Surah Najm, 38).