He was asked:

Concerning a man who went to sleep in a state of major ritual impurity and did not awaken until shortly before sunrise: he feared bathing with cold water in cold weather, but if he heated the water, the prayer time would end. May he delay the prayer until he can bathe, or should he perform dry ablution and pray?

He answered:

Scholars hold two opinions on this issue. The majority, including Abū Hanīfah, al-Shāfi‘ī and Ahmad, require him to seek water, even if he prays after sunrise. Mālik requires him to perform dry ablution and pray within the prescribed time, because observing the prescribed time takes precedence over the other obligations of prayer. The evidence for this is that, if he awakens within the prescribed time and knows that he will not find water until after it ends, then, by the consensus of the Muslims, he must perform dry ablution and pray within that time, rather than bathe and pray after it has ended.

Those holding the first opinion distinguish this case and similar cases from the situation in the question on the grounds that the obligation to pray applies to him only when he awakens, as the Prophet, may Allah bless him and grant him peace, said:

“Whoever sleeps through a prayer or forgets it, let him pray it when he remembers it.”

Since he is only commanded to perform it after awakening, he must perform it in accordance with what he is able to do