Is it permissible to perform tayammum in order to pray Fajr on time if the weather is cold after having intercourse with one's spouse at night?

It is not permissible to perform tayammum merely due to cold weather as long as water can be used by warming it or similar means, because the means to an obligation is also an obligation. However, if it is highly probable that using water will harm you and cause illness, then tayammum is permissible, based on the Hadith of Amr ibn al-Aas (may Allah be pleased with him) when he performed tayammum on a cold night fearing perishing after he had a wet dream, and the Prophet (peace be upon him) approved of his action. It is obligatory to perform the prayer on time with purity. If a legitimate impediment, such as the inability to use water, prevents it, then one should perform tayammum and pray, and their prayer will be valid.