Is hell a mercy and a punishment given that the Prophet, sallallaahu ‘alayhi wa sallam, said that there is healing in cauterization, which may be similiar to hell? And Allaah says that His mercy embraces all things, and hell purifies sins, and you probably will not feel bored. An open mind makes one wonder about these things. Please give me a specific and satisfying answer. May Allaah Almighty reward you.

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

Both the worldly fire and  Hellfire in the Hereafter share the quality of causing pain. However, Hellfire is much more painful, and it is sheer punishment for the disbelievers and the disobedient; Allah, The Exalted, says (what means): {And whoever disobeys Allah and His Messenger and transgresses His limits - He will put him into the Fire to abide eternally therein, and he will have a humiliating punishment.} [Quran 4:14] Since the Hereafter is the abode of recompense, Hellfire is sheer punishment. Abu Hurayrah, may Allah be pleased with him, reported that the Prophet, sallallahu ‘alayhi wa sallam, said, “Hellfire and Paradise fell into dispute, and Hellfire said, ‘I have been distinguished with the proud and the tyrants.’ Paradise said, ‘Why is it that only the weak and the humble amongst the people and the downtrodden and the simple enter me?’ Thereupon, Allah said to Paradise, ‘You are My mercy whereby I show mercy to those of My servants whom I wish,’ and He said to Hellfire, ‘You are My punishment whereby I punish those of My servants whom l wish.’” [Muslim]

The worldly fire has benefits for the people; it is one of the blessings bestowed by Allah upon His slaves and one of the signs of His Omnipotence. He has reminded the people of His blessings as He says (what means): {And have you seen the fire that you ignite? Is it you who produced its tree, or are We the producer? We have made it a reminder and provision for the travelers.} [Quran 56:71-73] This is in addition to the many other benefits of fire that we know of, including cauterization, as the questioner underlined; Ibn ‘Abbaas, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, said, “Healing is in three things: a gulp of honey, the scalpel of a cupper (i.e. Hijaamah), and branding with fire (cauterizing). But I forbid my followers to use (cauterization) branding with fire.” [Al-Bukhaari]

Al-Munaawi wrote, “The Prophet, sallallahu ‘alayhi wa sallam, forbade cauterization because it involves torture, so it must not be opted for except for a necessity. This is why the Arab proverb goes, ‘Cauterization is medicine's last resort.’” [Faydh Al-Qadeer]

It should be noted that the Muslim should ask only about the matters that lead to doing good deeds, as this is more beneficial and better for him. It is worthier of the Muslim not to ask unnecessary questions about matters that do not lead to doing deeds. We ask Allah to guide us and you to the path of truth.

Allah knows best.