What is the ruling on delaying ghusl and prayer until after sunrise due to severe cold? And what is the expiation for that?

A person in a state of major ritual impurity (junub) must hasten to perform ghusl (definition) (full ritual bath) in order to observe the Fajr prayer with complete purity. If he is unable to use water due to its coldness, he must heat it. If he strongly believes that he will fall ill even after heating the water and despite the availability of heating means, then he is permitted to perform tayammum (definition) (dry ablution) and pray within the prescribed time. He must then perform ghusl with water once the impediment is removed.

If a person in a state of major ritual impurity performs tayammum only, despite being able to use water (even with ordinary difficulty), and then performs ghusl after the time for prayer has elapsed and repeats the prayer, he is sinful for praying without proper purification, and sinful for delaying the prayer beyond its prescribed time. He must immediately repent, regret his action, and resolve not to repeat it in the future. There is no expiation other than this.