What is the ruling on performing tayammum when water is unpleasantly cold, but does not cause severe pain?

Tayammum is only permissible for one who cannot find water or is unable to use it for fear of illness. Mere coldness of water does not permit tayammum unless it leads to illness. And whoever performs tayammum merely because the water is unpleasant and does not cause illness, then his prayer is invalid and must be repeated.