What is the ruling on one who delayed ghusl for janabah—resulting from a wet dream—until Dhuhr prayer due to housing conditions and cold weather, and then prayed Fajr and Dhuhr after performing ghusl?

It is not permissible to delay the Fajr prayer beyond its time, and whoever does so intentionally is sinful. The person in a state of ritual impurity (junub) must perform ghusl (definition) (ritual bath) to pray Fajr, or perform tayammum (definition) (dry ablution) if unable to perform ghusl due to a legitimate Shari'ah-approved excuse. They should then pray Fajr with tayammum and not delay it, and there is no need for them to repeat it afterward. The evidence for this is the hadith (definition) of Amr ibn al-'As, the action of the Prophet, peace and blessings be upon him, and the statement of Sheikh al-Islam Ibn Taymiyyah.