Is the mentioned Hadith about Khalid ibn al-Walid, concerning the extinguishing of the fire of Hell by patiently enduring calamities in this world, authentic, and does it contradict the Almighty's saying: "Whenever it subsides, We will increase their blaze"?

No evidence has been found to prove that "the cooling down of Hellfire" is a Hadith. The Quranic texts affirm that Hellfire will not cool down for the disbelievers who are to abide therein eternally. This is supported by:

1. "Indeed, those who disbelieve in Our verses – We will drive them into a Fire. Every time their skins are roasted through, We will replace them with other skins so that they may taste the punishment. Indeed, Allah is ever Exalted in Might and Wise." (An-Nisa: 56).

2. "Every time it subsides, We will increase them in blazing fire." (Al-Isra: 97).

3. "The Fire of Allah, [eternally] fueled, which mounts to the hearts. Indeed, it shall be closed over them, in extended columns." (Al-Humazah).