This is only allowed on the condition that he can find no one to heat it, or is unable to use the public bathrooms. 'Amr ibn al-'Aas narrated that he was participating in an expedition. He had a wet dream during an extremely cold night, and was afraid that if he performed ghusl he would die. He prayed the morning prayer with his companions. He then went to the Messenger of Allah, upon whom be peace, to ask him about this. Muhammad said, "O 'Amr, did you pray with your companions while you needed a post-nocturnal bath?" 'Amr mentioned the verse, "Do not kill yourselves, Allah is merciful to you" to the Prophet. The Prophet just laughed and didn't say anything. (Related by Ahmad, Abu Dawud, al-Hakim, ad-Daraqutni, Ibn Hibban and al-Bukhari in mu'allaq form.) This example illustrated the Prophet's tacit approval.
If one fears for his life, family, wealth, (for example, if an enemy is nearby--beast or human--or one is a prisoner, and so on), one may perform tayammum. This is also allowed if there is water but one lacks the proper means to get it, or if one fears some accusation against him if he gets it.
This could be for a hound, for dough, cooking or to remove an impurity that is not pardonable. Says Imam Ahmad, "Many of the companions performed tayammum to save their water for drinking." 'Ali said that a man who is travelling and becomes unclean because of sex or a wet dream can perform tayammum if he fears he will go thirsty: "He should perform tayammum and not ghusl." (Related by ad-Daraqutni.) Says Ibn Taimiyyah, "If a person needs to relieve himself but has only a small amount of water, it is best that he pray with tayammum and relieve himself, rather than keep his ablution and pray before relieving himself."