Is the Hadith authentic which mentions that Allah casts His Hearing and Sight upon the inhabitants of the Earth during intense heat, and that whoever says "There is no god but Allah, how intense is the heat of this day, O Allah, protect me from the heat of Hellfire" will be rewarded by Allah and protected from the heat of Hellfire?

The aforementioned Hadith is weak. It was mentioned in "Kashf al-Khafa wa Muzil al-Ilbas" that Ibn al-Sunni and Abu Nu'aym narrated it with a weak chain of transmission. It states that if a servant says, "There is no god but Allah, how intense is the heat of this day, O Allah, protect me from the heat of Hell," then Allah will protect him from its heat. And if he says, "There is no god but Allah, how intense is the cold of this day, O Allah, protect me from the bitter cold (zamhareer) of Hell," then Allah will protect him from its bitter cold. Al-Albani classified it as "Munkar" (denounced).