CuTi was irradiated with 1-MeV Ne+, Kr+, and Xe+ in the temperature range from 150 to 563 K. The volume fraction of the amorphous phase produced during room temperature irradiation with Ne+ and Kr+ ions was determined as a function of ion dose from measurements of the integrated intensity of the diffuse ring in electron diffraction patterns. The results, analyzed by Gibbons’ model, indicate that direct amorphization occurs along a single ion track with Kr+, but the overlapping of three ion tracks is necessary for amorphization with Ne+. The critical temperature for amorphization increases with increasing projectile mass from electron to Ne+ to Kr+. However, the critical temperatures for Kr+ and Xe+ irradiations were found to be identical, and very close to the thermal crystallization temperature of an amorphous zone embedded in the crystalline matrix. Using the present observations, relationships between the amorphization kinetics and the displacement density along the ion track, and between the critical temperature and the stability of the irradiation-induced damage, are discussed.