Is this Hadith authentic?
Sayyidah ‘Aaishah (radiyallahu ‘anha) says that Rasulullah (sallallahu ‘alayhi wa sallam) had a cloth that he would use to dry off with after wudu. (Tirmidhi)
Imam Tirmidhi (rahimahullah) has recorded this narration as cited in your question. He has declared the Hadith weak (حديث عائشة ليس بالقائم ولا يصح عن النبي صلى الله عليه وسلم في هذا الباب شيء).
(Sunan Tirmidhi, Hadith: 53)
The Hadith is corroborated and is suitable to quote.
(Refer: Sunan Tirmidhi, Hadith: 54, Tuhfatul Ahwadhi, Hadith: 53 and Badhlul Majhud, Hadith: 245)
And Allah Ta’ala Knows best.
Answered by: Moulana Suhail Motala
Approved by: Moulana Muhammad Abasoomar, with the following note:
However, it should be noted that there were occasions wherein Nabi (sallallahu ‘alayhi wasallam) didn’t use a towel after Wudu/Ghusl as well. (Sahih Bukhari)
Therefore both are correct.