I say, with Allah's guidance: It is permissible for him to perform tayammum, and thirst is considered a valid excuse for tayammum. Ali, may Allah be pleased with him, said regarding a man who is traveling and becomes in a state of major ritual impurity with a small amount of water fearing thirst: "He performs tayammum and does not perform ghusl," as mentioned in Sunan al-Daraqutni 1: 202. See: Al-Muhit p.317, Sharh al-Wiqayah p.106, and Umdat al-Ri'ayah 1: 96, and Allah knows best.