Indeed, the cooling [delaying] of the Dhuhr prayer during extreme heat was only established to ward off the hardship that would be even greater if the cooling [delay] were applied to the Friday prayer.

Section: If an Eid coincides with a Friday, attendance of the Friday prayer is dropped for the one who performed the Eid prayer, except for the Imam, for it is not dropped for him unless he does not (14) have those who can pray the Friday prayer with him. It is said that there are two narrations regarding its obligation upon the Imam. Among those who said it is dropped are al-Sha'bi, al-Nakha'i, and al-Awza'i. It is also said that this is the view of 'Umar, 'Uthman, 'Ali, Sa'id, Ibn 'Umar, Ibn 'Abbas, and Ibn al-Zubayr. Most jurists said the Friday prayer is obligatory due to the generality of the verse and the reports indicating its obligation, and because they are two obligatory prayers, so one does not replace the other, like Dhuhr with Eid. Our evidence is what Iyas ibn Abi Ramlah al-Shami narrated, saying: I witnessed Mu'awiyah asking Zayd ibn Arqam: Did you witness two Eids gather on one day with the Messenger of Allah (peace and blessings of Allah be upon him)? He said: Yes. He asked: How did he act? He said: He performed the Eid prayer, then granted a concession regarding the Friday prayer, saying: "Whoever wishes to pray [it], let him pray." Recorded by Abu Dawud, and recorded (15) by Imam Ahmad, and his wording is: "Whoever wishes to perform the Friday prayer, let him perform it" (16). From Abu Hurayrah, from the Messenger of Allah (peace and blessings of Allah be upon him), who said: "Two Eids have gathered for you on this day of yours; whoever wishes, it suffices him [instead] of the Friday prayer, and we are performing the Friday prayer." Recorded (17) by Ibn Majah (18). Similar [narrations] from Ibn 'Umar and Ibn 'Abbas from the Prophet (peace and blessings of Allah be upon him). And because the Friday prayer only exceeds the Dhuhr prayer