Is it permissible for a man to pray alone at home with his chest uncovered, or in a congregation with his wife, especially when the summer heat intensifies?

Performing congregational prayer is an individual obligation for adult, capable men, and it is not permissible to abstain from it without a legitimate excuse. Even a blind person who cannot find a guide is not permitted to abstain if he hears the call to prayer. The presence of heat is not an excuse for abstaining from the congregation as long as it is within one's capacity.

As for a man praying with an uncovered chest, his prayer is valid according to the majority of scholars, who cite the hadith (definition) of Jabir (may Allah be pleased with him): "If the garment is wide, cross its ends over; and if it is narrow, use it as an izar (waist wrapper)." This means that one who prays wearing only an izar will have an uncovered chest, and his prayer is valid. Nevertheless, it is better and more preferable for a Muslim to pray in his finest appearance and clothing, in compliance with the words of Allah Almighty: "O Children of Adam, take your adornment at every masjid." Some scholars are of the opinion that it is obligatory to place a part of the garment over one of the shoulders, and that the prayer of one who prays without anything on his shoulder is not valid if he is capable, citing the hadith: "None of you should pray in a single garment, with nothing on his shoulder."