The ruling on tayammum (dry ablution with clean earth) in the case of severe cold while traveling

Question:
May Allah reward you. Honorable Shaykh, this questioner says: We went on an outing, my family and I, to the desert. When we got up to pray the Fajr (dawn) prayer, the weather was very cold, so much so that we were shivering from the cold. I endured the cold and performed wudu' (the ablution for prayer), but the rest of the family resorted to tayammum (dry ablution with clean earth). The question is: What is the ruling on their action?

Answer:
If they have something to heat the water with, such as gas or firewood, it is not permissible for them to perform tayammum (dry ablution with clean earth); rather, they should heat the water and perform wudu' (the ablution for prayer). However, if they have nothing to heat the water with and the water is cold and unbearable, there is no harm in performing tayammum (dry ablution with clean earth). This is what 'Amr ibn al-'As (may Allah be pleased with him) did while traveling when he experienced a wet dream; he performed tayammum (dry ablution with clean earth) and did not take a ghusl (the full ritual bath). He mentioned this to the Prophet (peace and blessings be upon him), and the Prophet approved of it. Yes.