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As long as the person is in his own domicile and not on a journey in open country, then he is obliged to perform a full bath (ghusl). He should take whatever precautions he must take in order to prevent injury or bodily harm, such as heating up the water.

If he is in open country and is unable to heat up the water and he fears that by waiting he will miss the time for prayer and he has a legitimate fear of physical harm besetting him if he uses the water to perform wudû’ or ghusl, then he may perform tayammum and offer his prayers.

He may not, in any event, postpone his morning prayer until the time of the Zuhr prayer as long as he is in possession of his rational faculties.

`Amr b. al-`As, while leading a military campaign, once woke up after having a wet dream. He had suffered an inflicted wound earlier and feared that performing ghusl would cause him injury. Instead, he performed tayammum and then led those who were with him in their morning prayers. They learned of this and brought the matter up with the Prophet (peace be upon him), who turned to `Amr b. al-`As and said: “O `Amr, did you lead your companions in prayer while you were in a state of major ritual impurity?”

`Amr replied: “O Messenger of Allah! I had remembered Allah’s words: ‘Do not kill yourselves. Indeed Allah is to you most merciful’.”

Thereupon the Prophet (peace be upon him) laughed and said nothing further. [Sunan Abî Dâwûd (334) and Musnad Ahmad (17812)]

This hadîth shows that the Prophet (peace be upon him) had approved of what `Amr b. al-`As had done.

However, as for someone living in a home environment where he is able to heat up the water and cover himself with blankets, he may neither postpone his prayer nor resort to tayammum.

And Allah knows best.

Source: Islam Today