I was wondering; is there a consensus among the scholars of Hadith not to use hadiths declared Hasan (good) by At-Tirmidhi as Hujjah (authority)?

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Dear brother, you have sent us so many questions about Mustalah Al-Hadeeth (Hadeeth terminology) that they seem to be infinite in number! We have previously underlined that the fatwa section is not concerned with teaching students or helping researchers; rather, it is mainly concerned with issuing fatwas for those who need to know the rulings of the Shariah on the matters that concern them. We have previously advised you to study this discipline at the hands of a specialized scholar. We hope that you would act upon our advice and that this would be your last question about Mustalah Al-Hadeeth.

As for your question, many researching Hadeeth scholars held that most of the ahaadeeth classified as Hasan by At-Tirmithi are prone to be weak. Ath-Thahabi said in Al-Meezaan,  "One should not be deceived by At-Tirmithi's declaration of a hadeeth as Hasan, as after investigation, most of them turn out to be weak."

He even criticized the ahaadeeth he declared as Saheeh (authentic), saying, "Scholars do not rely on At-Tirmithi's declaration of a hadeeth as Saheeh."

Al-Albaani said:

"Regarding At-Tirmithi's classification of a hadeeth as Hasan, it is not reliable, especially after identifying the ʻIllah (subtle hidden defect identified by versed Hadeeth scholars, deeming the hadeeth weak while on the surface it may seem authentic). In fact, At-Tirmithi was one of the Hadeeth scholars who were considered lenient when it comes to classifying ahaadeeth as Saheeh, like Al-Haakim, Ibn Khuzaymah, and Ibn Hibbaan. This is why Ath-Thahabi said in Al-Meezaan (p. 33), 'Scholars do not rely on At-Tirmithi's classification of ahaadeeth as Saheeh.'"

Apparently, there is no consensus among the scholars on this matter. In his book Masaadir As-Sunnah wa Manaahij Musannifeeha, Dr. Haatim Ash-Shareef said:

"Al-ʻIraaqi refuted this statement in his commentary on Jaamiʻ At-Tirmithi. He said, 'The statement that some scholars do not rely on At-Tirmithi's classification of ahaadeeth as Saheeh is not correct, as they have always relied on his Saheeh classification.' Those were Al-ʻIraaqi's words in refutation of Ath-Thahabi. Also, Ibn As-Salaah stated that At-Tirmithi's classification of ahaadeeth as Saheeh is accepted when he mentioned Saheeh Al-Bukhaari and Saheeh Muslim; he said: 'There are more Saheeh ahaadeeth that were not cited in Saheeh Al-Bukhaari and Saheeh Muslim. These Saheeh ahaadeeth could be found in a number of Hadeeth collections,' and he mentioned At-Tirmithi's compilation of Saheeh ahaadeeth among them. So Ibn As-Salaah as well stated that he relied on At-Tirmithi's classification of ahaadeeth as Saheeh."

In his book Tahreer ʻUloom Al-Hadeeth, Al-Judayʻ said, "Prominent Hadeeth scholars after At-Tirmithi have been accepting his classification of ahaadeeth as Saheeh or Hasan unless it is proven wrong. This is the most appropriate attitude towards a Hadeeth scholar who studied at the hands of Al-Bukhaari, Ad-Daarimi, and Abu Zarʻah Ar-Raazi."

Ibn Al-Wazeer said in Tanqeeh Al-Anthaar:

"The statement of Ath-Thahabi indicates the permissibility of relying on At-Tirmithi's classification of ahaadeeth as Saheeh and Hasan given the consensus upon his trustworthiness and memorization in general... As for Ath-Thahabi's statement that 'scholars do not rely on his classification of ahaadeeth as Saheeh,' then perhaps he meant by it that they do not rely on his Saheeh classification of ahaadeeth narrated on the authority of Katheer ibn ʻAbdullah, as this is stated in some versions (of his book Al-Meezaan)."

Allah knows best.