Must one who performed tayammum for the Fajr prayer, fearing the cold, despite being able to heat water, repeat the prayer?

Tayammum (definition) is not permissible except when one is unable to warm the water and would be harmed by using it. As for bearable hardship, it does not permit tayammum. And whoever abandons the use of water and prays with tayammum, their prayer is invalid and must be repeated. They are sinful for performing the prayer without purification while being able to do so, and it is as if they never prayed at all for abandoning a condition of prayer while being able to fulfill it. The Prophet, peace and blessings be upon him, said: "Allah does not accept a prayer without purification."

Tayammum is not permissible to resort to except when water is unavailable or there is a fear of harm from using it.